Well, what you can wield with one hand is determined by weight, and is perhaps determined by your current strength (at the time of wielding).
If you have a zweilhander equipped before you bust your hand up you can continue to do so just fine after. albeit slowly.
If you try to wield a shotgun after your hand busts it will deny you.
And if you ever break both hands but live Id suggest never unequipping your current weapon until it fixes.