$.02 again:

I have to disagree with Shooter - IMO tumblers aren't that expensive. You can get one around $50 or so online, the media will run you about $20 for corn cob and walnut (check pet stores to get it for less), and the wax is break even since you'd need it with any other polishing device. So for $100 you're definitely set up. A variable speed dremel starts at, what, $75? Before you get all the extra stuff...

I think Undream and Fingers are right about the risks of a dremel. It's easy to let the dremel slip and hit the razor, and it only gets easier as you increase the RPMs. I've seen videos of people going pretty willy-nilly with a dremel, too - hand tightening the bits and pushing the limits of the tool. The whole thing is pretty unstable. Hit your finger with a 60 grit piece of SP going at 10,000 RPMs if you don't believe me.

As for putting a razor in a tumbler with the scales on, I wouldn't. A few reasons: It won't be able to clean or polish the pivot in between the scales, and adding some sort of "rig" will only cover more of the razor and leave "tumbler lines." The razor could move around and put some forces on the pivot area or scales that might break them. If you've ever unpinned scales (poorly) you know how fragile celluloid/bakelite scales are. And the biggest reason for me, if the scales are that important not to risk unpinning the razor, why would I throw the scales into a tumbler?