I am delighted to let you know that I HAVE skinned a cat. (As biology / physiology students have been doing since Hippocrates.) I would say that the main consideration is what you want the dead cat for.
If you primarily want the fur, a la Cruella DeVil, then you want a method to harvest it that preserves the hide intact. Strangulation or drowning in a sack would be good practical choices. Beating is risky, better to use rat poison and broken glass (hidden in its feed).
If you are after the meat, and don’t mind getting the hide messed up, then you can use stabbing or projectile weapons. Obviously avoid poisons, and drowning would cause technical complications you don’t want to get into.
And if you simply want to torture the poor animal, then apply skin-devouring insects that will allow the cat to live for weeks in agony.
(I never liked Hippocrates much anyway!)