The age-old time-tested way to clean a fur is simply to lay it flat on table and rub plain yellow cornmeal into the hair. The cornmeal will adsorb the dirt, dust, etc from the fur hairs, thus leaving the fur clean. To remove the cornmeal from fur, just shake it like you would a rug. It comes out easily, leaving fur clean and fresh. Sawdust from hardwood trees can be used instead of cornmeal; however, cornmeal is better (you don't want pine/spruce/etc sawdust because of the resins).

If you have a tumbler, you can tumble the fur in cornmeal. One way to tumble a fur is to put it into a waterproof bag such as the ones that we use to keep stuff dry while kayaking and canoeing http://www.thewaterproofstore.com/bags.html and tumble it in your household clothes dryer, making sure to set the temperature to air/fluff (no heat).

Here is a reference that contains information about the use of cornmeal to clean fur, and there is other information regarding hides furs,and skins:

http://www.state.tn.us/twra/pdfs/tanninghides.pdf