Try T-cut, I've used it on a valued Steve Reich CD which was scratched by my car autochanger and it works fine on my CD transport now. Follow up with something like Reveel.
Removing scratches on CD's
I have fine scratches on some of my CD's. Is there any way to restore them to new condition? Would like to restore them to a mirror finish again. None are skipping... yet, but would like to take care of this so as not to have the error correction circuitry kick in. Have found that the do it yourself, cheap, scratch removers put some really fine swirls on the finish. Any suggestions?