This summer there have been quite a few cases of cats shot with airguns, and surviving that long enough for someone to find out, and bring in police and press.
Denmark is a .177 FAC country
Mind you these are probably shot with a anemic springer.
Cat population can some times get out of hand in some places, but you just call someone and they come ( free of charge ) and trap them and do,,,,,,, whatever.
Not really a need to go " hunting "
Mind you my friend, at his old place he had a Koi pond, and stocked with quite a few fish, and he lost some to a cat, and the owners of the cat could not care when he confronted them.
So,,,,,,, in the end sadly cat had to go.
As i recall the law here actually state that you got to keep your cat on your own land,,,,,, which is not at all easy if it is not in a harness and roped up, which again with a cat can be quite problematic.