Cougars, bears and "the occasional stray pitbull" just aren't much of a threat. And 'flares" aren't much of a defense. In other words your defense is primarily a security blanket, a mental crutch. In the event of an actual attack by the time you could deploy a flare the event would be over. You would be better off with a Louisville Slugger. A simple, effective and vastly underestimated device against man and beast alike.

Possibly the best move would be to talk to the local wildlife officers and either get advice, possibly reassurance that there is really little actual risk, and possible some advice to overcome your fear. The best defense against fear are facts and understanding. Or advice and recommendations on devices you might carry.

I suspect your best bet may be a large can of strong pepper spray.