Cats will do what is instinctive for them, the same as dogs, birds, crayfish or any other animal. That is no excuse for random cruelty.
I don't see the need to license bows, for the simple reason that any untutored person can pick up a gun or crossbow and kill someone at least at short range. Somebody picking up a bow for the first time is more likely to hurt themselves than anyone else.
Besides, banning or controlling things doesn't always work. Handguns were banned many years ago, resulting in sporting shooters giving up or moving abroad, yet what difference has it made to gun crime? Even if you could control any particular weapon, the thugs will use something else. A piece of wood with a nail in it - should we then license wood and nails?