decision on cat

Four years ago there was a cat sleeping in a propagation box on the front poarch, witch was not in use at the time.I had opened the front door, without seeing, or disturbing the cat.When he awoke he peered in the oped door, through the storm door, and I said " honey, there is a cat peeping in the window", and as you moved to see him he would move to avoid us.This was the beginning of a free "meal ticket" for the cat, and he did this manuver every time he was hungry.Find a window where he could see us, and peep in.We named him "tigger", but I wanted to call him "peeping tom"DW won out, so we named him tigger.About eight days ago , he came to a window, and was dragging his right front paw.We rented a trap from the animal shelter, for only $5.00, and he was easy to catch, and now we are facing a big decission.
(1)have him put down
(2)amutate the leg, and nutter him
(3)take him to the UGA vet school, and have the shattered leg fixed, and that would require much more trouble, because he is wild, and will only get within sight when he is hungry.
BTW, I owe this deed due to an unconcerned neighbor who says any animal get on my property, it gets shot, witch is what happened to Tigger.We don't know how a "wild" cat can function with three legs.Your opinion please. Mike