I usually just do clitoral stimulation while on my period, but you could just throw a dark towel under you and be fine i think.

When I'm having really bad cramps, an orgasm can help relax my muscles and make the cramps less intense. However, I've had a few times when I wasn't experiencing any cramps at all, and then I orgamsed and that brought the cramps on. It's weird, but it always makes me weigh the pros and cons before I start masturbating on my period.