You and I both have hands that don't like wool! I've been tempted to knit with gloves on so I can keep my nails when I'm doing something for felting.
Dollar stores have rolls of thin rubber matting meant for drawer liner, shelf cover, etc. They are GREAT for use under table runners, vases that can get bumped, etc.--anything you don't actually want to stick down with tape or museum wax. The matting lasts for years and is easy to clean if it gets dirty (I use it on top of our freezer because the cats like to lie there.) It shouldn't be a problem on any modern finish, either. All you have to do is cut a piece slightly smalkler than the runner and arrange the runner on top of it.