I used to give Jasper the option before we went to bed I'd check to see which door he stopped at the pantry/larder door for food or the side door to be let out. There were occasions when he wanted to go out but the weather helped to change his mind
Jasper had been shot too when he was a young cat. The pellet was resting on his spine, it didn't cause him any problems fortunately; and the vet said it would be too risky to try and remove it.
I understand why you won't let him out but chances are the idiot(s) will have grown up or moved away. Just a thought.
Sue