There are plenty of big cats in mtns of western Wyoming. Check with some people around DuBois Wy and/or Cody.
The last 2 years hunting Elk in the Absaroka range out there, we've crossed pretty big fresh mtn. lion tracks from the day or night before we've gone through areas next to dark heavy timber. Not exactly what we want to see, as it keeps you looking up and around more for them and grizzlies than you'd like to.
Better go with outfitter that has plenty of experience and good dogs. One of the fellows we talked with who runs a hotel in DuBois does and seemed to be careful of when to follow and when not to follow big cats. I've heard they will try to draw their pursuers into tight spots where they can see and have the advantage. Guys and dogs can get in trouble that ends bad, if not careful. That's all I know.