Also,, there is no wolf introduction in the San Juans or anywhere in that vicinity. And coyotes are not federally protected. In most of the west they can be shot on sight as a varmint.
Mountain lions and feral dogs are the biggest threat to any sheep out there.
And also, your use of quotes around the word “tourists” indicates you know little about that area. Tourism is THE industry there. Nothing else comes close.
In winter every snow sport you’ve ever heard of happens there. In the summer the area is filled with jeeps and 4x4s, and serious hikers and climbers from all around the country.
In the fall, the deer and elk hunters arrive. There are huge numbers of legitimate tourists all in those forests who can easily encounter those sheep. When they fill the road in front of you, you shouldnt have to deal with a menacing cur. This is a new addition to the scene.
Just don’t shoot a dog because he barks at you is all I’d say. That’s what cops are for, I understand.