I'm curious to know if your WG piece is originally rhodium plated by Cartier and needs re plating or is it an unplated piece that you wish to rhodium plate OP?
If it helps at all my Love bracelet was purchased pre owned from Collector Square in Paris (I wanted the original screw system) and had been rhodium plated either by them or a previous owner.
A lot of second hand vendors seemed to do the same when I was shopping around. Probably to make the item look bright, new and shiny!
I then took it to Cartier to have a personal engraving added on the inside.
After a couple of years it started to wear and if there's one thing I hate it's worn rhodium plating (I sold a Bvlgari ring for the same reason, but that's another story!)
As I happen to like the unplated white gold from Cartier I had my local jeweller polish off the remainder of the rhodium. He had originally intended to just remove the rhodium from the outside as he was concerned about losing the engraving too, but told me it looked really weird with rhodium on the inside but not outside as it was then two toned.. he removed all of it on both sides in the end and the engraving was absolutely fine!
Hopefully that helps, however if your piece was originally plated by Cartier I would definitely ask them to do it first and if it wasn't rhodium plated in the first place, personally I wouldn't do it.. especially as I think you said it was a ring, which will wear again and will require re plating again in the future.