I appreciate your concern about taking care of this humanely. Believe me, I have experience in this area. (Don't worry - the bat is out of the question. If the incident was any worse, then i'd have done it with my bare hands)

I used to work as a vet assistant and had to put a few animals down. The procedure is very quick and humane. The problem I found is that most animals KNOW about the Vet hospital and that is one of their biggest fears. Killing a dog that is scared to death and often peeing on the ground when you try to restrain and inject the needle hardly seems humane. (except to the elderly couple in the lobby - who did not actually see it happen)
On the contray, my dog loves to go on walks and run in the woods. On such an trip and instant tap (by the proper calibur gun) to the brain would be very clean and very humane in my book. And I have done this to a 13yr old German Shepherd a few years ago who was in a lot of pain and could no longer walk (just about 20 feet before resting, then another 20, resting, ... you could see the pain and frustration in her tired old eyes).
It was not a pleasant experience - convulsions, some blood, ect, but instant and done out in the woods where she loved to be. It was the right thing to do (if it were me, that's how I'd want it done).