In my opinion, if you are going to trap a problem animal, the most responsible thing would be to kill it humanely. You have said that you are not an animal abuser, but abuse is exactly what it would be if you put it in the garbage to slowly die a terrible death. Let it out of the cage where you trapped it, and it will just continue to do what it has been doing. Let it loose somewhere else, and it will become someone else's problem. Can you think of any other options?