Just a few thoughts...
I haven't tried stamping directly on a usable CD... yet... but I don't see any reason you couldn't.. and maybe even emboss on it as well... so long as you didn't have to heat it enough to warp the CD. To me, it seems this would work because the CD is played from the bottom side anyway. Not sure how much clearance you have above the CD in a player though... or what added weight might do.
CD's aren't all that expensive, maybe you could burn one, decorate it... and just see what happens? (if it would stlll play)
You also might just purchase some CD labels... like you create with your computer... and stamp those instead... the kind of ink wouldn't be so important this way because you could always spray seal it before applying to your CD.
Good luck... HAVE FUN... and maybe just experiment and share with the rest of us what you find