You really do need to raise it with HR or your managers. Physical harassment like this is unacceptable on any level. It's not "tattling", overstepping or being weak or inappropriate. In its own way, you are also doing HIM a disservice by letting him get away with it - he will get the message that this is an OK way to behave and it's best for everyone, including him, if he learns this lesson at the beginning of his career, before he goes on to do worse, at your company or elsewhere. Any reference he gets for future jobs (including, maybe even especially the military) needs to be accurate too, and if he is a liability or a danger to colleagues then future employers may need to know about that.
Can you go back to the managers who assigned you his work for a discreet chat? You could say something like:
"Chris, thank you for assigning me XYZ project and the ABC task, I'm enjoying working on them. However, unfortunately, since I've started working on them, in the last few days Jon seems to have picked up on this and has begun going deliberately out of his way to barge into me or strike me. He shoulder barged me yesterday when walking past me, despite me having enough room behind me for him to not do that. Today he saw I was behind him and purposely rolled his chair backwards to bump into me. He also keeps making snide comments about my appearance - hair colour, weight, etc.
I'm finding this very uncomfortable and I would appreciate your advice in how we can manage this. I know that Jon is possibly only going to be with us for a few months longer, but his behaviour is becoming distracting and a real cause for concern. I would be grateful for your support in stopping it so that I can concentrate on my work without having to worry about Jon's intimidation."
Any decent manager (or, frankly, human) would want to know about this, so that it can be reigned in. You say your managers and colleagues praise you for your work and you sound like a good employee, I'm sure they would be sorry to hear that you are being subjected to this behaviour and would want to support you.
It is not being a troublemaker; it's bringing a legitimate concern to managers who have the ability to put a stop to it. They may even appreciate you even more for having the courage to speak up and trust them with your concerns.
Hope things get better for you soon. x