You might get lucky and the trim be far enough away from the bulb to stay intact, but don’t risk it. Hot glue is never a good idea on any lamp part. Tacky Glue (or Ultra-Tacky) works much better, doesn’t melt.

Also, a tip for painting wooden balls: I took a scrap of wood and nailed some large nails into it. I stick my wood balls onto these nails and paint that way. You can spin them around and touch up places, hands-free, and let dry there.