I have to say that I do find some issues with your post. Setting up a campsite with all sorts of firearms and trip wires doesn't seem to be conquering any sort of irrational fear. Perhaps derfending yourself from a rational fear, yes, but not an irrational fear. If these said bears and cougars pose a rational threat to your welfare and you are in a situation that requires you to be within their striking distance (although it seems unlikely), then perhaps you could justify setting up traps to protect yourself from them would be acceptable. However, voluntarily putting yourself in harms way for no apparent reason other than to say you did it, in my opinion, does not justify causing harm to innocents. I understand and have no issue with killing an animal for food, but to enter their domain and kill them with a gun just because you can makes no sense to me.
I have an irrational fear of spiders. My wife has to remove them from the house if I see them. If she does not do so in a timely manner I will destroy them. Do they actually pose a threat to me? Probably not. But my fear won't allow me to capture them alive and set them outside. This is my agreement with her. I would not however, walk into the woods and set myself in the midst of a bunch of spiders with the purpose of killing them in their homes. If I see a spiders web I would do all there is to avoid it but if there were a spider that somehow found its way on me than I would freak out and who knows what would happen.
Anyhow, (orgive me as I ramble), I don't see the need to conquer a rational fear, and conquering an irrational fear is not done by setting up booby traps for it.