The stuff (decade or more in age?) is likely too brittle to come off in one piece, and certainly not easily. Suggest you reglue any lifting edges, mask off the wrap and sand / paint the rims.

So if I fix and mask up the wrap, I should be sanding very carefully?? And is spray painting still the easier way to go. I think I read that on here somewhere.

If you mask it, spray painting will work just fine. Just remember that 4 light passes are better than 1 heavy pass. Light sanding with 4-0 steel wool between passes. Use a razor knife to removed any exess glue first.

I know this post is about a month old, but I just painted a couple of bass drum hoops two days ago. They were from a low end set of Mapex and the paint was chipped in a number of places. I sanded them down until they were smooth then sprayed them using a good gloss black paint from a rattle can. I took a thin piece of wood and ran a sharp wood screw through it so the tip of the screw was showing about 1". I hung the hoop on point of the screw and painted about 1/2 of the outside, or as much as I could reach without turning the can upside down. Then did the same on the inside. Wait about 10 minutes and turn the hoop 180 degrees and repeat the process. I put about 4 coats on and they turned out looking very nice.

They didn't have any wrap in the center like my Rogers hoops did and I had to refinish them once because of chipping. I attempted to remove the wrap but it was so brittle, the set was from the early '70, it started breaking. I carefully glued the pieces back on then covered it with painters masking tape. That type of tape isn't real sticky so there is little chance of it pulling the wrap off. Careful sanding and painting and the Rogers hoops came out looking like new. I made sure where the cracks in the wrap were visible were under one of the claws.