Of course you're not alone with this.

When I was dating, what helped me was planning out ahead of time what to say (plans always make me feel safer). So when I was still getting to know someone, I would give clear social cues that it was not to be discussed: "Those are from a bad incident I was in, I don't like to talk about it." I planned to repeat myself if pressed, but all inquiries stopped there.

When I dated someone quite seriously, at a certain point it became important that he know the truth to see the real me, and I simply said, "I used to cut myself." He was very accepting. Now, with more maturity and insight, I would probably flesh out my answer: "It happened at a very sad and lonely time in my life when I struggled with tragedy and had no idea how to cope with my feelings."