I found a site, Cougar Info, that lists confirmed cougar attacks and there have been people who've successfully defended themselves against a cougar with only a knife, for example:

61-year-old David Parker was attacked by a 100 pound (45 Kg) adult, male cougar at about 7:30 p.m. on his nightly stroll along a road near his home about two kilometres outside of Port Alice ... As the cat clawed and bit into his neck, face, and head, Parker managed to open his knife's three-inch blade, stab the cougar a few times, and eventually slit its throat, leaving the cat to bleed in the middle of the gravel road.

A Moscow, Idaho man, unwilling to be identified, reported he was attacked by a mountain lion at about 6:00 in the evening while camping southwest of Elk River, Idaho ... During the struggle, the victim grabbed a knife and stabbed the mountain lion in the side, causing it to run into the timber.

That said, there have been cases where knives have been used, but didn't seem to have as effective as hoped.

After reviewing these accounts, I'd wager a solid fixed blade would give you an above average chance of surviving a cougar attack. I've also seen recommendations for using bear spray as a defensive tool against cougars.

Actually, this same site has some good do's & don'ts for avoiding and/or surviving a cougar encounter and regarding weapons it says:

Use anything available as a weapon if the lion displays aggression but generally not if you must turn your back, crouch, kneel, or bend over to get one

• Carry mace or pepper spray where you can easily reach it
• Use fists, sticks, rocks, tools, a pocket knife, a bicycle, whatever you can hit with, throw, and/or use as a shield
• Target an eye with your thumbs, fingers, or a weapon

Fortunately, cougar attacks seem as rare, if not rarer, than bear attacks.