Is it textured where the scuffs are? If the scuffs are not too deep you can 'Lightly' wet sand it with 500-600 grit [try to only remove the raised portion of the scuff you feel with your fingers, go too far and you lose the texture] and paint it. For a chipped corner I would use SEM® Problem Plastic Repair [autobody supply store]
If your 63 SS console is like most of them, it's pitted as well as marred. These were cast in pot metal which is notorious for pitting. To fix cracks or broken edges that will accept chroming likely will require a professional pot metal repair. Because of all the long, tight grooves, these consoles are almost impossible to restore as original. Just rechroming will make the pitting appear even worse. You could spend a ton of money on repair and still not have a satisfactory result. My suggestion is to clean up the 2 pieces as best you can and stay on the lookout for better ones. I found a rear piece that was considerably better than the one that came in my car. These consoles appear quite often on Ebay and at swap meets.