Alas, after couple hours of strenuous research yesterday, I admit that this question is hard to answer but is capable of being deduced upon since one cannot speak for the general public. Thus, I came down with the similar conclusion as CDR.
Unfortunately, I was only able to find French and English articles instead of the desired German articles. Below are three quotes from articles published around 1888-1918 which alludes to the Kaiser's crippled arm before his abdication.
In the first article seemingly published in 1918, the article states:
The last time I saw Dick we decided the best way to end this war was
for us to challenge the Kaiser and the Crown Prince to a doubles match
in Berlin. We figured this out after learning that the Kaiser had a
crippled arm and the Crown Prince never played the game. Dick says
that with a month's hard practice we could give them a hell of a run
The second article created in 1894 states:
The Kaiser's crippled arm does not prevent his being an excellent shot, and he takes great pride in bringing in a fine bag of game.-Harper's Bazar.
The French article created in 1888 states:
Wilhelm a l'uniforme des hussards rouges, dont il est le colonel effectif. Il est grand et fort, mais du tronc robuste, désagréable surprise, se détache un bras d'infirme, atrophié par suite d'un arrêt de développement et qu'il porte généralement devant lui comme s'il était paralysé."
"Wilhelm wears the uniform of the Red Hussars, of which he is the effective colonel. He's tall and strong, but from the robust trunk, an unpleasant surprise, stands out a crippled arm, atrophied as a result of arrested development and which he generally carries in front of him as if paralyzed."
Excerpts from a letter by Charles Gibson (1867-1944) to American journalist George Creel (1876-1953) in February 1918:
“Charles Dana Gibson enthusiastically passed on a suggestion to Creel: too many pictures in the press presented a youthful, vigorous kaiser; better to show his crippled left arm and “sinister countenance.” “Flattering pictures of the Kaiser,” he advised, “should be discouraged.” Creel agreed.”
Source: Manipulating the Masses by John Maxwell Hamilton pg. 236
Conclusion: People were cognizant of Wilhem’s arm, however to try to answer for the general public would be fatuous since there’s not much sources willing to help us on that. It would thus seem that majority of the people would've known that he had a crippled arm by the virtue of those sources above. Thus, as CDR said, it would seem that "it was definitely common knowledge by the time his reign came to an end."