my dad and his friends use to hunt cats, they always used a .22 mag pistol and shot them in the head once they had been treed, you can't even tell where the hole was on the mounts.

if you're not hunting with dogs i'd say the .243 is a good choice, use a light bullet with limited expansion to minimize damage to the hide.

if worst comes to worse shoot them twice with that .243, you don't need repellent.