I don't think Wyoming let's non residents trap without a fur dealers licensei didn't dig into it a whole lot, but when I did a couple years ago, I couldn't find any regs that spelled it out clearly.
Probably best to ask a Warden about that one.
I have given thought to it myself, and still on the fence about the idea.
But, I likely won't have time to hunt deer or elk and run traps. Not to mention skin the catches and flesh and store the hides for the trip home.
Lots of coyotes out there in the areas I hunted in Wyoming though.
Probably easier to set up a day or two and try to call in a few.
If you find something out though please share what they tell you.