I wouldn't worry much about the animals, but I follow common practices. Mt lions would be somewhat a concern for me if traveling alone. National or state park websites should have info on animal safety. You only have to worry about black bears. I don't know how many are in tat area, but some common sense practices are don't have food in your tent, or clothes that may have had food spilled on them.

I can't advise on tethering as that isn't something I have done. You are the parent, safety is your responsibility. You know the kid and what he's like and if it will likely be a problem. If you don't think it would be safe don't take him there, simple as that. Think about what you would have to live with if something happened to him, or what he would do if something happened to you. My son was smart enough when he was 8 to follow instructions and not do something dangerous if I explained the situation, unless maybe he was with a group of kids. Of course I have no idea of the place or actual risk involved and I haven't been to AZ yet.