When they were sold with the eyes glued in, I removed them before painting. I used nail polish remover. Just a drop or two is all that was needed to loosen the glue. However, it’s still “dangerous” to remove the eyes. You can chip the eye sockets. But I would use a tiny tiny flat head to remove the eyes.
Do what you feel would be easier for you. If you’re afraid that you’ll break the eye socket if you try to remove the eyes, then just mask the eyes off or paint carefully around them.