Mika,
Aside from my intense fondness for teak, I agree that it would be a shame to paint over perfectly good veneer. (Although I understand your interest in your system matching.)
I did the reverse with my Beomaster 4500 which arrived with the white trim, while everything else in my “collection” is rosewood. (Except the Beogram 4000 & 4004) I used perfectly ordinary rosewood contact paper (available at Home Depot) and covered the white trim to extraordinarily good results. (It looks like the veneer on my Beogram 4002.)
I got the courage to do this after a friend insisted on gifting me with a pair of S-45 speakers which had the white covering which was badly chipped and yellowed in the California sun. The speakers were in great acoustic shape, just looked sad. So I tried the contact paper on them and honest to God, they look like the real deal.
I was afraid they would look tacky…. you know “genuine imitation fake wood.” But I figured if it came out badly, I could always remove the contact paper.
As for your 1962 Cadillac, KEEP IT ORIGINAL. I had a 1959 Cadillac Coupe de Ville for over 25 years and I did everything in my power to keep it as original as the day it left the factory.
Best wishes with all your toys!
Jeff