Similar to Jenna, with smaller kids I usually just say I had an accident and it was scary, and i don't like talking about it. Then I ask them if they've ever had any accidents.
Especially when it's family, it can be tricky. I know when my cousins were young for example, I had to sit down with my aunt and uncle and ask how they wanted me to handle it and what they thought was age appropriate to say. Now my cousins are both in college and while I've never explicitly told them, they do know that they're self harm scars, but they're not judgemental about it.
I agree with having a plan, but when it is something like family, you may also need to make sure to check first to see what their parents are okay with you sharing and how. In public it's a lot easier to say that it's private or personal, or just from an accident.
I don't think you have to ignore or shy away from the pain. You can say that it is from a bad or scary time in your life, and that it's hard for you to talk about. There's definitely ways to do that which can be age appropriate and not be too explicit.