The class was aimed at domestic animals. I should have referenced that. :-) Although a cougar is not a domestic animal, its bite is about the size of a large dog.
I wouldn’t do it other than in complete unarmed (first mistake) desparation. The advice usually includes grabbing the tongue to induce a gag reflex. Guess it’s better to lose an arm than your head, but I question the effectiveness. I’d go with a firearm or spray.
The problem with cats and bears is that unlike a dog, they have lots of weapons besides teeth.
Cats will likely disembowel you with their back feet if you get a hold of their tongue or frustrate their bite.
I like the frying pan option.