When you don’t want to reconnect

What do you do when you hurt someone to the point that they end a relationship with you, but then later on, they’re the one who wants to be friends with you again (or get back together, or otherwise start being part of each other’s lives again), but facing up to what you did makes you feel really bad and you just want to move on without being in each other’s lives?
Is there any way to say, “I think we’re better off not in each other’s lives” without hurting them even more?
First and foremost, it’s ok to decide not to resume the relationship. You don’t have to have a relationship you don’t want to have, even if the reason it initially ended is that you hurt the other person.
It’s probably not possible to completely avoid hurting them, because rejection always hurts. It’s painful to want to have a relationship that someone else doesn’t want, especially if there’s a loaded emotional history. You probably can’t prevent that hurt entirely.
But, saying no to a relationship you don’t want is not the same kind of hurt that you caused by whatever you did before. (Even if it’s triggering because of what you did before, which happens sometimes.)
What you can do is avoid being cruel about it, and avoid sending mixed messages. You could maybe say something like, “I’m sorry that I hurt you, and I hope you’re doing well. At this point, I don’t think it’s a good idea for us to be interacting.”