That would totally work! I would consider yourself lucky that you came up on that. You can buy plastic dowel sleeves or covers online. They come in various sizes and would be removable so you could put them in a bucket of sanitizer then slip them over the dowels when your about to use the rack. Or you could sleeve the dowels with food grade hose and just put some star San in a spray bottle prior to using the rack. Just spray the dowels that are covered with the hose. Obviously you would want to buy hose that created a snug fit. As for the plastic covers, they should be loose so they are easy to take off and on.
Good luck! Send a pic when it's done.