Cougars are hard to spot because they are half-transparent and they initiate combat very fast to a player target nearby.
It is very dangerous to fight cougars in the open, because their stun will most likely override yours. It is better to stun them while you stand behind obstacles and when they are stunned run close to them to make a more powerful attack. Then repeat.
With the Hideworking skill, skinning a single Cougar will yield:
Random chance to get various rare items from butchering. Chance of dropping, and sometimes also the potential quantity, is much higher with Viscera & Bits.