Well,
I am not so sure about that. If he wasn´t in the German Luftstreitkräfte from the get go, he might have been enlisted in an infantry regiment from Hamburg, got wounded, was declared unfit for infantry service at the front and switched to the FA33. This happened quite often. However upon checking the German loss-list there was no candidate that seemed likely. There was one Droth from Lübeck who got wounded...
I think it is more likely he got the Hanseatenkreuz for helping out some unit of Hamburg origin with his service.
GreyC