Is there a standard of professionalism in academia requiring me to hide self-harm scars if I'm otherwise comfortable leaving them exposed?
You should do what you are comfortable with. If you want to keep them hidden, that is fine. If you want to sometimes wear clothes that reveal them, go ahead, assuming the clothes are otherwise appropriate. Your colleagues will probably not care, and if they do, they need to - and will - get over it.

I would caution that letting students know your history could be problematic, in that it could increase the likelihood that they come to you about personal issues. No matter how supportive you are, no one wants more students dropping by to talk about personal problems.