USCutter sells a ground strap that hangs from the cutter and lays on the vinyl that would work for you here. You could also just make one, it's nothing more than a wire and some magnets to hold it in place.
The key is to ground the vinyl, doesn't really matter if the stand is grounded or not, but with a metal stand it's easiest to ground the stand which then in turn grounds the vinyl that is sitting on it.