I've had great success using Scrubbing Bubbles to clean satin wraps.

Don't wax and don't polish..

Yep... Scrubbing Bubbles will get down in the little grooves and lift out the dirt.

My 66's were a total disaster when I picked them up from a garage sale for minimal dollars. I think it was 3... maybe 4... serious cleanings with a deep cleaning spray on cleaner and they were flashing like the aurora borealis!