After some pondering, I decided to remove the drawer guides and paint everything. I decided it would be no more effort to drill out the pop rivets than it would to tape around the guides. They are all just secured with one rivet each. The guides in the base are pop riveted, but the drawer guides have hollow rivets. They lock in with tabs and would probably work without rivets, but I think that pop rivets won't stick out enough in the drawers to make any problems.
I'm considering painting the insides of the drawers with truck bed spray paint. It is tough as nails, won't scratch or chip and will provide a non-slip surface inside the drawers. Plus, it cures very hard and fast. Paint can take months.