If you have a queen you're unhappy with, start a nuc. That way if the new queen is not accepted or another hive goes queenless, you have a solution at hand. A queen doesn't really do her best production until years 2 and 3 so replacing a queen every year, IMO, is executing her just as she becomes most valuable. Let hives do natural supercedure, you will end up with a queen that is probably just as good, if not better, than what you would buy. If you must remove a queen start a nuc and keep her as an emergency solution elsewhere in your bee yard.
I wouldn't kill a weak queen until late fall and then I'd combine the nuc she was in with one of the weaker hives.