I would not use my deer tag to shoot a wolf, just buy a wolf tag, they're cheap.
I would shoot a mtn lion using my deer tag because they are so rare to see without hiring an outfitter with dogs. After you shoot a lion and tag it with your deer tag you can still go buy a second deer tag to finish out your hunt.
Honestly, I wish that IDFG would just give a free wolf tag to every non-resident hunter purchasing a deer or elk tag.
As for those who struggle with the ethics of killing something you are not going to eat. I think you should reconsider that decision. The primary utility of most prey animals we hunt is meat. Since that is what most of us hunt we were raised to make the best use of the meat. The primary utility of predators is fur, it's a completely different thing. Saying you won't shoot a wolf becasue you can't eat it is like saying you won't shoot a deer because you won't use it's hide for clothing.