Simple answer: no.
The premise of the question is flawed, probably in more than just one way.
Danes did not sack Hamburg in 983, and Hamburg most probably wasn't destroyed in 983 at all by anyone.
- 880 third destruction of Hamburg, by Norman and Slavic raiders, led by Eric the Child
- 915 fourth destruction of Hamburg, by Danes and Slavs
- 1012 fifth and complete destruction of Hamburg, Wendish led by Mistivoi
— Hellmut Elers: "Chronologie und Calendarium der Geschichte Hamburg's", Oncken: Hamburg, 1868. (p5–7, own translation, excerpts, gBooks)
This already eliminates the date of 983. That the name given for the leading man responsible is still problematic will be explained later.
That there is an error arising from some of the chroniclers is noted quite early on in critical historiography:
Annalista saxo praecipiens tempora ad annum 983 direptionem Hamburgi a Mistevojo perpatratam enarrat, quae rectius anno 1012 jungantur.
— Johann L. Gebhardi: "Origines Serenissimorvm Dvcvm Meclenburgicorvm Docvmentorvm Avtoritate Assertae", Schroeder: Brunswick, 1762. (all sic!, p18, gBooks)
No contemporary record exists from that year mentioning such an event. On the contrary, record keeping and document production seems to have continued uninterrupted throughout 983. But such documentary evidence is then broken off at a later date, 1012.
In 983, however, in that broad region, a Lutizen (Veleti, Liutici) revolt, also called Slavic revolt, took hold. Curiously, most often without much traces left in the archaeological record of many towns said to have been destroyed at that time.
The most often found connection of 'Hamburg destroyed in 983' — like the easily repeated hearsay that is Wikipedia — is said to be connected to Mistivoy, the Nakonid prince of the Obodrites.
That is not probable. Scholarly research even debates fiercely whether that tribe was partaking at the revolt at all, which took place mainly a bit upriver and on the right bank of the Elbe and its hinterland. Mistivoy is now to the contrary most often seen as much more of an Empire's ally ("reichsnah") than an enemy. It is certain that in 984 Mistivoy was on very friendly terms with his alleged 'German'/Saxon enemies and still mentally healthy.
What seems to be much more clear is that Hamburg was indeed completely destroyed in 915 by Obodrites and again in 1012. Which would then mean Mistivoy's son Mitislav would be responsible for that. Record keeping then dies down in the town for a while, there is an extensive layer of destruction found, and in the 1020s the Hammaburg III structures were newly built.
There are numerous hints from circumstantial evidence to historical notices and archaeological finds that make any complete destruction of Hamburg for the year 983 highly unlikely, and the next best date with a confirmed catastrophe for that small town is only to be found in 1012.
Around that time, starting in 1012, the chronicler Thietmar von Merseburg describes the Slavic Revolt in 983 and also mentions en passant the destruction of Hamburg. Many seem to infer from that he meant Hamburg to have fallen victim to those events then. But we can find only traces of very small scale raids. Since Thietmar writes with an agenda and describes Mistivoy as so mentally ill as to have required being hold in chains, this is quite obviously an exaggeration, tainting the probable veracity of the whole account on this.
Wikipedia is notoriously unreliable.
Even if we look at the German version for the History of Hamburg, we see the claim repeated: "Mistvoy's Obodrites ransack Hamburg in 983".
But looking at the page for Mistvoy himself, we come closer to current historical scholarship:
Slavic Uprising of 983
The Slavic Revolt of 983 represented an uprising of the Slavic tribes united in the Lutizenbund against the tribute rule of Margrave Dietrich of Haldensleben. On June 29, 983, the Lutizes first destroyed the bishop's seat in Havelberg and three days later also conquered Brandenburg, the seat of the margrave. Thus the imperial dominion east of the Elbe was destroyed for decades.
Mistivoy is said to have taken part in the uprising on the side of the Lutizes by devastating northern Albingia, burning Hamburg, destroying the bishopric of Oldenburg and finally destroying the Benedictine monastery in Kalbe (Milde) far south of his domain in the Altmark.
A passage from the Slavonic chronicle of the chronicler Helmold von Bosau, written 200 years after the events, is cited as evidence of Mistiwoj's participation in the Lutizian uprising. According to it, immediately before the uprising, Mistivoy visited the Lutsk tribal sanctuary in Rethra to tell the tribes gathered there about the serious insult by Dietrich of Haldensleben. At the request of the Lutizes he had renounced the Saxons. Helmold then describes Mistivoj's campaign of destruction. In contrast, in the research on the history of the Abodrites, reservations have always been expressed against Mistivoj's participation in the Slavic uprising in 983, since such a participation cannot be reconciled with his politics before and after the uprising.
Destruction of Hamburg
However, about 40 years after the Slavic uprising, the historian Thietmar of Merseburg had already stated in connection with the Slavic attacks on Havelberg and Brandenburg that Mistivoj had burned down and devastated the bishop's seat in Hamburg.
However, there are doubts whether the attack on Hamburg coincided with the Lutsk uprising of 983. The description of Mistivoy's attack on Hamburg in the context of the Slavic uprising does not necessarily describe two simultaneous events, especially since Thietmar did not intend a description of the Slavic uprising.
Rather, he was concerned with an enumeration of all those attacks against Christianity that followed the dissolution of the bishopric of Merseburg in 981, which in his opinion was unlawful. In addition, according to a later comment by Thietmar, Mistiwoj subsequently went mad because of his actions, so that he had to be kept on a chain.
In 984, however, according to Thietmar's report, Mistiwoj took part in Henry the Quarrelsome's Easter Court Day in Quedlinburg - and apparently well in his senses. And in Hamburg the episcopal document activity stopped only around the year 1014, which would have been expected earlier with a deserted bishop's seat. Moreover, in none of the contemporary annals and chronicles is a Slavic raid on Hamburg recorded for the year 983. In contrast, Adam of Bremen in his Hamburg church history clearly reports a devastation of northern Albingen and a destruction of Hamburg by the Abodrites, which took place after the year 983, possibly even under Mistivoy's son Mistislav in the year 1012.
In English almost summarized as:
These plots will be developed in another story dedicated to the raid of the
Obodrite duke Mstivoy who attacked Hamburg, although it most certainly did not have much to do with the rebellion in 983. Thietmar combines a description of a town fire with a miraculous event: in the middle of the flames a golden right hand appeared from heaven to lift and save the relics of saints. The chronicler emphasizes that the miracle happened in a place where a bishopric formerly had been located, and this in a sense connected Hamburg with Merseburg, which had also lost the rank of bishopric capital. Thus this moment that stoked the chronicler’s empathy could have influenced his will to show appreciation for Hamburg in the pages of the chronicle by mentioning this miracle, but it would not be his only motivation.
The admiration of the army for this supernatural intervention in the narrative was accompanied by fear of the Obodrite duke, Mstivoy, who ultimately became insane, which seems a trite motif in descriptions of people who stood out against God. However, when shortly before his death he was sprinkled with holy water – most certainly as a form of exorcism – he reacted by shouting that he was being burnt by St. Lawrence, which referred to an earlier description of the Slavic raid of the monastery in Kalbe, which had this saint as its patron. Mstivoy’s insanity and his abandonment to the fate of demonic powers, in the perspective of the chronicle, appears to be punishment for the destruction of the said monastery as a display of vengeance from God himself and his saint.
The chronicler did not mention the fact that the Obodrite duke participated in the raid that devastated Kalbe. He attracted the revenge of God, and especially St. Lawrence, only for his role in the community of those who assailed the Church, the core of which was the rebellious Slavs from 983. In this context it is especially worth remembering St. Lawrence’s special role as protector of Merseburg. The cathedral in this town was dedicated to him, and the bishopric there was founded by Otto I out of gratitude for victory over a dozen years earlier in the battle on the Lech River (955). Hence Thietmar created an image of the patron saint of his own diocese as an intercessor ensuring the effective protection for the Saxons in the time of war.
Relevant footnote, listing other sources than me below, but again in agreement with deferring the date of destruction:
Most probably Mstivoy’s attack of Hamburg took place a few years later, see Labuda, “Powstania Słowian,” pp. 169, 192 f.; Babij, Wojskowość, p. 139. See also below, pp. 235 f.
Going back to the Side of the Danes in 983: Among the most important sources we again look at Thietmar and Adam of Bremen. Adam's account is of similar quality compared to Thietmar. Including people, dates and places; in this case Danish king Harald Bluetooth expanding Danish rule and re-taking Hedeby:
Some of this has enjoyed the general acceptance of later historians. It is normally accepted that […] Harald sought refuge with friends in Jumne and died there on the 1st of November sometime around 985, and certainly no later than 987; […] There is, however, little reason to believe any of this or anything else in Adam's story. Adam's History of the Archbishops of Hamburg was conceived and written as part of Hamburg's struggle to preserve its position in Scandinavia; it served the same purpose as the forgeries produced at about the same time by Adam's colleagues in the archiepiscopal scriptorium, those very documents that he refers to in his text.
An analysis of Adam's information leaves little to be trusted. […] He has transferred the wars fought in 973-74 between Otto II and Harald Bluetooth and in 983, when after the death of Otto II Harald Bluetooth with Slav allies attacked Hamburg, to this earlier time, thus concealing the uncomfortable fact that his would-be saint accepted Christianity at a much later stage in his career and, worse, not from Hamburg-Bremen. He also, and this was no less important, established a claim that Hamburg deserved all credit for introducing Christianity in Denmark against claims made by Hamburg's arch-enemy the archbishop of Cologne that his see had a share in it. Cologne was, of course, demanding the return of Bremen to the archdiocese of Cologne from which it was taken after the sack of Hamburg in 845. This would severely threaten the very existence of the archdiocese of Hamburg.
Adam's next information on Harald relates to the 980s; it is basically a lot of fanciful information, among it a claim that Harald conquered England (ii 25). This particular information is given to demonstrate the contrast between kings on God's side, who expand and conquer other nations, and those who are against God and therefore lose their lands and suffer miserable exile, or worse. It is a clear example of Adam's putting the higher truth before historical truth, […]
— Niels Lund: "Harald Bluetooth - A Saint very nearly made by Adam of Bremen", in: Judith Jesch (ed): "The Scandinavians From The Vendel Period To The Tenth Century. An Ethnographic Perspective", Boydell Press: San Marino, 2002. (p303–320)
— Kerstin Schulmeyer-Ahl: "Der Anfang vom Ende der Ottonen. Konstitutionsbedingungen historiographischer Nachrichten in der Chronik Thietmars von Merseburg", DeGruyter: Berlin 2009, p247. doi
— Bernhard Friedmann: "Untersuchungen zur Geschichte des abodritischen Fürstentums bis zum Ende des 10. Jahrhunderts" Duncker & Humblot: Berlin, 1986), p259–272. — David Fraesdorff: "Der barbarische Norden: Vorstellungen und Fremdheitskategorien bei Rimbert, Thietmar von Merseburg, Adam von Bremen und Helmold von Bosau", Orbis mediaevalis. Vorstellungswelten des Mittelalters, Vol 5, Akademie Verlag: Berlin, 2005. doi
— Stanislaw Rosik: "The Slavic Religion in the Light of 11th- and 12th-Century German Chronicles (Thietmar, Adam of Bremen, Helmold of Bosau): Studies on the Christian Interpretation of Pre-Christian Cults and Beliefs in the Middle Ages", East Central and Eastern Europe in the Middle Ages, 450–1450, Vol 60, Brill: Leiden, Boston, 2020. doi
— Lorenz Weinrich: "Der Slawenaufstand von 983 in der Darstellung des Bischof Thietmar von Merseburg", in: Dieter Berg & Hans-Werner Goetz (eds): "Historiographia Mediaevalis. Studien zur Geschichtsschreibung und Quellenkunde des Mittelalters. Festschrift für Franz-Josef Schmale zum 65. Geburtstag", Darmstadt 1988, p77–87. dnb, regesta imperii
— Fred Ruchhöft: "Vom slawischen Stammesgebiet zur deutschen Vogtei. Die Entwicklung der Territorien in Ostholstein, Lauenburg, Mecklenburg und Vorpommern im Mittelalter" (Archäologie und Geschichte im Ostseeraum. Vol 4), Leidorf: Rahden 2008, p126. dnb
— Jens Schneeweiß: "Zwischen den Welten. Archäologie einer europäischen Grenzregion zwischen Sachsen, Slawen, Franken und Dänen", Wachholtz Verlag: Kiel, Hamburg, 2020. doi