Many years ago I had a similar problem with a plastic tank. I took a shoe brush (who remembers them?) and without adding any polish and just using whatever had stuck to the bristles I scrunched it circular fashion on the face with the grooves.
Worked well. Never had a problem as I thought might happen with the wax. Films loaded slickly.
I have had success with using a soft artists brush and brushing in a very tiny amount of Mr Sheen furniture polish then cleaning it out with another brush.
"People who say things won't work are a dime a dozen. People who figure out how to make things work are worth a fortune" - Dave Rat.