I don't like the idea of giving the Hansa German for precisely the reasons DrBob pointed out. They are supposed to have low manpower, and aren't supposed to expand much in Europe. They are a trading and then colonial power. In wars, their defense is their fleet, and the fact that their holdings are far-flung, preventing anyone without a navy from successfully taking them on.
Giving the Hansa German culture is simply an invitation for them to go on a land conquest adventure in Germany. While they are weaker than Bavaria or the Order, they can still easily take on the 1 or 2 province minors that make up a significant portion of Germany. This places them in the unique role of being a colonizing nation with a large right-culture right-religion territory in which to expand.
Eire has only 3 (5 if you include Wales and Galicia) provinces with the right culture that they do not own at start, and 3 of them are likely to be wrong religion, and held by a strong opponent.
Sicily (once Italian is removed) has 1 (+2 in Africa through events).
Brittany has to make a choice between two secondary cultures, and faces strong opponents in taking either.
Al-Andalus has to deal with the crusade, and there is only 1 Andalusi province they don't own at start. They have Arabic, but that is far from their usual area of expansion and on a different continent besides. (Personally, I don't think Al-Andalus should have Arabic anyways.)
Genoa has to face Milan and the Pope if it wants to expand in Italy.
Giving Hansa German culture would be giving them too much power that they can easily consolidate in the early game. In a way, they become like Russia in AGCEEP, if Russia was in the Latin tech group from 1419 and Siberia was filled with BTV 8 Sugar provinces.
Hence the dilemma.
Hanseatic culture is bollocks, German culture releases an unwanted beast.
There is a third (and fourth) option.
Hansa has no culture group.
This reflects its urban, port-town burgher support base, and that - actually - they ought not to have all that rural countryside of the provinces we have no choice but to give them.
This would restrict their Manpower, but that's the point, right, we don't want them to gain a lot of manpower.
It would mean high stab costs, which seems appropriate for such an organization, so far flung.
So they'd need to spend all that cash on mercenaries, which is very very realistic, and encourage them to avoid wars at (almost) all costs. At least until they colonize.
That's where the next problem would come in. We can't have new world provinces with no culture. Doesn't make any sense. But presumably these places would be multi-ethnic with a strong german slant, or else each colony might be dominated by a particular culture within the league.
So, here would be the solution (requiring a lot of coding from me).
Each time the Hansa establish a colony, they'd get the choice of what culture group it would be: German, Baltic, Scandinavian or Italian. Neither much matters to them, so no doubt a player will have some fun with it.
To balance the challenge of having no right culture provinces, each province they own could have an even granting it a permanent -1 RR (or -2).