If the female cats are safely secured during the night, why not lay out a proverbial carpet of spring action rodent traps in front of the door?
So, you want to shoot a cat for being a....cat? I dunno...how about locking the cat door for a little while. It'll learn very quickly its food supply is cut off and go elsewhere.
A BB gun (or paintball gun) won't permanently hurt a cat (unless you shoot it in the eye). I agree that locking the cat door is the best thing, though.
A BB can penetrate a cats skin and a paintball can break it's ribs, neither should used unless the shooter wish's to kill the cat, and in that case they should use a firearm that kills it quickly so it doesn't suffer until dying with broken ribs or a steel pellet in it's lung.
This thread is three years old. But FWIW, the solution is to use RFID a cat door. Only your cat can come through. https://www.amazon.com/s?k=rfid+cat...590812&tag=googhydr-20&ref=pd_sl_4j27vqoz4x_e
Depends on the state, but I know that shooting strays with a paintball gun can get you a year or more for animal abuse. It's a Class E felony in Indiana. Also, under Indiana law, if an animal is injured by an intentional unprovoked attack (meaning that the animal wasn't endangering you or your propertly to injury or damage at the time you harmed it), and you are convicted, you are required to pay all costs of treating the animals out of pocket.