you should take em off for painting Chris, end of story. Whatever damage you presume may happen by taking them off is fixable.
if your car has factory side skirts, they are most likely held on by clips, a few screws, and a very minimal amount of double sided type adhesive. They are quite easy to remove.
If you have aftermarket skirts on, they have probably been slapped on with sikaflex and maybe a few screws that are out of the usual sight of the car - eg in the wheel arches