The real problem is the political infrastructure. The Hansa had nothing like a central decisionmaking body, funds, or military. Everything depended on the will of individual city governments to cooperate. Any colonial venture would most likely take the shape of ca privileged Kontor, a trading entrepot where merchants could do business, rather than a territorial claim. What would a Hansa city do with territory? It's not like they lacked land at home. People, on the other hand, could always be got. Most Hansa cities were demographic sinks, encouraging immigration from relatively far afield and assimilating newcomers readily. Add another pull factor and you get more people coming. What they couldn't do is forcbler settlements. There weren't enough undesireables around.
Regrettably, Hamburg is not a terribly good candidate despite its geographic location. Due to its territorial commitments on the mainland and its efforts to arrogate the status of an imperial city, it was in theory a belligerent every time the emperor went to war. That kind of thing was not lost on the French. If I had to be creative, Cologne might just stand half a chance. Navigation down the Rhine, good relations with the Estates General, and a heavily industrialised and populous hinterland. Not to mention money.