Try tumbling them in a mesh bag in the drier in small batches with fabric softner sheets. That may get off the cat hair. If not, take a basin of water and a table outside. Cover the table with a sheet. Rinse a few at a time and lay them out on the sheet to dry--not on a windy day, of course. Refresh water as needed and the small pieces will dry quickly. If you are worried about fading, after the tabletop is full of pieces, cover with another sheet. They should dry fast in your Texas sunshine.