Perhaps some iron wool or a brillo pad would be better....
Don't forget the final polish with a sanding wheel.
Seriously, though, I have used CloneCD to copy a non-Windows-readable CD. (Just out of curiosity I copied an SGI IRIX install CD -- worked fine -- including boot info) The thing to remember, though, is you are making a bit-for-bit copy of the original CD. If the original comes up with unreadable areas on the read, your cloned CD will have a "best guess" of those errors written to it. My thought is that you will probably end up with a perfect copy of a coaster. Of course, blank CDs are so cheap, it's probably worth a try, anyhow.