I have used some of these vortex monoculars and they are very nice. They are probably what i would bring on a trip like that. It'll go on your belt or in a pocket.
Your binoculars are fine. Don’t expect to see anything like a wolf or a bear. People will immediately turn stupid and move (run) towards the animal trying to get a picture, chasing it off.
At yellow stone last year there was a coyote crossing the road. While I was trying to get a picture some idiot ran, ran 100 yards towards it with a camera with a telephoto lens at least a foot long, causing it to run off, ruining the photo opportunity for the 15 others stopped on the road to see it.
You'll see plenty of wildlife in the parks. But not in the middle of the day, and not within half a mile of the road. Get up early, go hike unused trails, and get away from people.
Vortex binoculars would be a fine choice. They're razor line was on sale over the winter, I should have grabbed a pair. So would $100 Bushnell ones, though.