Of course it's "overkill" but so is the 25-06. Both are much more cartridge than what is needed to kill deer and smaller animals. But dead is dead. The question is how muc recoil do you want to put up with when shooting these smaller game animals.

My choice would be the .243 long before the 25-06 if for no other reason than ammo availablilty. The .243 is available in more stores and is factory loaded with bullets specifically designed for varmints as well as deer. Much harder to find a varmint bullet in the 25-06.