I think you can talk about potential Moorish influences on Iberian nautical expansion in following three areas:
By the 9th/10th Century, al-Andalus (Islamic Spain + Portugal) was by far the most advanced and wealthiest part of Western or Central Europe. When the northern Christian kingdoms expanded south, they were generally conquering places that were wealthier, more populous, and more (for example) agriculturally sophisticated, and they were able to profit from this. This undoubtedly contributed to the relative wealth of 15th Century Portugal and Aragon/Castille/Spain -- though by then other parts of Western Europe were probably equally wealthy.
Science and Technology
Starting in the 12th Century, Christian Europeans started translating (or commissioning translations by Muslim and Jewish scholars of) Arabic works of philosophy, mathematics, and science. (This included the considerable expansion on ancient Greek knowlege carried out by Arab and Persian scholars, in addition to the actual ancient Greek works that had been translated into Arabic.) Most of this took place in Spain, in the newly conquered bits under Christian control, though some also took place in southern Italy. This helped kick-start the first European universities (which is why some scholars refer to this as the "Twelfth Century Renaissance"). However, this new knowledge spread very rapidly throughout Western and Central Europe (part of it was scholars from places like France and Italy travelling to Iberia to request translations), so it wasn't as though the Iberian kingdoms had any sort of monopoly on this.
There's also the possibility that Northwest African naval technology -- and further developments in al-Andalus -- may have contributed to the development of the Portuguese caravel, which was so important for Iberian exploration. (There were other important technological developments that came to Europe from the Islamic lands, but those spread through the Mediterranean, and were at least as available to Italians as they were to Iberians, so it doesn't directly relate to "Moors in Iberia".)
(A side comment: when people talk about "the Renaissance" starting in Italy, they're referring to the Italian Renaissance, which did indeed start in Northern Italy in the 14th Century. This certainly built on the Twelfth Century Renaissance in some respects, but was a separate development; so saying that "the Renaissance started in Toledo, not Italy" isn't really correct.)
Expansionist spirit or ideology
Talking about historical "spirits" gets a bit dodgy, since it's very hard to agree on definitions or examples. Nonetheless, some people have argued that the enthusiastic, militant energy and expansion that characterized the Reconquista "spilled over" into the voyages of discovery (and subsequent conquests). In this sense, the Moors served mainly as an inspiring target...