Need Advise to Restore a 65 "wood grain" steering wheel

I had to remove/replace the retaining ring on the underside of my steering wheel while it was face down on my dining room table. This caused a lot of micro-dings and scratches which are almost invisible but I can feel them when I drive.
Can I just sand and polish the wheel? Is it brown plastic all the way through? Or, I am thinking I might paint it like it was originally. Were these wood grain wheels painted to look like wood or is that just what they were called? What paint would you use? Anybody have pictures of a restored or new one?