I've used Brasso on my 5G iPod. It's was good for removing shallow scratches and scuffs on the plastic. I didn't bother with deeper scratches because there are few of them and I don't want to remove too much plastic. Afterwards, I cleaned off Brasso residue with rubbing alcohol. When I carefully examined the screen afterwards I noticed that Brasso left a very slight haze. The haze wasn't noticeable in normal use.
I only did the entire iPod while it was disassembled. While the iPod was assembled, I only polished the screen because I didn't want anything to leak into the iPod.
If your player has painted surfaces, be careful with Brasso and rubbing alcohol. Both contain solvents which can damage some paint.