Was kind of hoping for a serious answer ._.
I just realized that you said hunting knife instead of hunting rifle. Well then I guess you could try making yourself smell like cougar shit or something and hope that the cougars won't attack something that smells like their own shit. If that doesn't work have a big lump of meat with you and trow it at the cougars if they attack and if that doesn't work then change your running route, you don't need to have a few mile long road, you can run around your house or local neighborhood for as long as you would normally do. With the all the info you provided this is the best I can do.
Unfortunately this is a gaming forum. You won't be finding animal experts here.
Speak for yourself, I had a dog once and used to have lots of bulls and cows, I know everything about animals.