The thought process behind this proposal is completely flawed.

Suppose that all air gun owners are licensed, and a cat gets shot near 99 Acacia Ave. It was shot with a .22 pellet.

Within a five mile radius of where the cat was shot there are seven licensed air gun owners, five of them have .22 calibre rifles.

So, we have five suspects, except we know and the coppers know that it is not licensed owners who shoot cats, so after wasting time and money inspecting the rifles and ammunition owned by the five people and finding that none of them own or use Bulldog pellets of the type removed from the cat, the Police are exactly nowhere in finding the moron that shot the cat.