Broncohauler

With a Teflon disc,  my TS hitch jaws wouldn't close around the pin of my Travel Supreme.  I wasn't able to find a thinner one.  Anything thin enough would be torn up by the wt of the hitch and the twisting while turning.

For 10 bucks or so, it's worth a try.  If 3/16" is a shade thick, you may be able to run it thru a thickness planer.  The Teflon or plastic won't damage the cutters.  I think 1/8" would be as thin as you could go without it getting destroyed by the hitch weight and turning. 

It would be worth a try to at least eliminate greasing the plate and inevitably transferring  to clothes.

https://www.etrailer.com/Accessories-and-Parts/Lippert-Components/LC286160.html

This one is 3/16", the thinnest I've found.  Others go up to .6"

With any plate, I'd be even more vigilant about making sure the jaws lock.  I'd hate to make UTubes epic failures.