Yes, some polishing rouge will do the trick. I highly recommend you mount the trim to a piece of scrap lumber, and screw that to something solid. Last thing you want is to catch an edge on the trim and have it go flying, or injure you.
To add to Chuck’s comment—he cautions against damaging the part or ‘yourself’. That last bit is pretty important as you can get hurt if not careful buffing with a wheel and rouge. that method yields a great result, but be careful in handling the part so the wheel doesn’t grab the part. If the wheel does grab the part, it may be best to let it go. The part can be replaced, fingers not so much. Wear some good gloves, take your time, and be careful.