I would say that checking for cuts is probably a little intrusive. If he has new ones, and he wants you to know, then he'll let you see them (it might not be blaringly obvious, like "look mum, here are some new cuts", it might just be that he wears a short sleeve t-shirt which may not hide them, or something).
Moving the stuff out of sight is fine, but I would say from my perspective, to know where something sharp is helps. For example, this week I am away on holiday, and I have a tool in my bag. It will probably be that I go through the entire week without using it, but knowing that it's there helps, because it gives me the option, and stops me feeling like I'm trapped in a situation.
Sitting next to a friend that knows about it will probably help too, because as you say he can let them know. When I was at school my teachers knew that I had MH issues, so in theory I could just stand up and walk out of any lesson, no questions asked. In fact, in the two years that I had the issues, I only did this once or twice, but again, knowing the option was there helped. It would probably then be useful to have somewhere he can go and be alone / quiet. Perhaps the school can suggest somewhere?
Hope this helps. I know I'm not / wasn't in the same situation as your son, but I figure if I tell you stuff from my POV, as a harmer, then it might help!