Have you seen a mountain lion (puma) attack? While you can survive an attack (since it has happened before) you sure as hell aint getting the upper hand You’re better off protecting your face and throat (because they will go for the kill) and attacking its sensitive spots like nose and eyes
Dogs are easier than cats yes because their teeth are their primary weapon but don’t think the claws can’t do damage I’ve had dogs draw blood from me during nail trims- and these are smaller than wild dogs And cats? Especially big cats can do a lot of damage even if you manage to get their head secure and that’s unlikely I’ve had my arm practically torn up while catching feral KITTENS and I had a house cat bite clean through a good chunk of my finger (that hurt like a BITCH btw)