I tried a pot scourer on a guitar neck once: took away the glossiness, but didn't quite have the slickness I wanted. So I took a nail-filling pad thing to it (basically fairly fine sand paper) to rough it up a lot more, then went over it with the scourer to buff out the scratches.
I'd try the scourer first (starting on a hidden spot) and see if you can get the result you want. You can always move to something courser after if it isn't working out, but you can't go back if you go too far from the start. Best to take it gently.