I don't think that you should lie and say that you are 'fine' but talk to him and reassure him that you aren't suicidal. That's assuming that you aren't? Even if you are it still might be an idea to talk to him about your feelings. It may be that he doesn't even notice the cuts etc and if he does he may not want to discuss it at all!
I know you say that he is 'only 20' so wouldn't be able to cope with it, I have to say I disagree with that. You're a year younger and you're dealing with the feelings that bring you to hurting yourself. He's a grown man so I'm pretty sure he could hack it.

xx