Just so you know, you don't even need to specify C or U when you use offset printing.
The U and the C are only paper "previews" of what you should expect. The ink used is generally the exact same color recipe but reacts differently depending on the stock used.
If you only have access to the good old paper Pantone book, you can always ask your printer to give you an equivalent for the color you chose. That's when you might want to specify U or C, to make sure you get something closer to the preview you see on your own Pantone book!
Also, when printing on plastic, it's possible you'll need to use another Pantone "book":
If it's on vinyl, it's possible it will be this one too (FASHION, HOME + INTERIORS):
Since these colors are used on many different materials that all react differently, a good way to see a good preview of the final result is to simply pay a visit to your printer and ask for samples. Some inks will react differently depending on the printing method you'll use and the kind of plastic (and its color) too. You should really ask your printer how to prepare your files and what Pantone system to use because it's possible you'll even need to plan your layout specifically for that printing method and add to it a white opaque base under your artwork. Unlike paper, printing on plastic is more a matter of opacity. But this can be something you incorporate in your designs as well, depending on the kind or plastic you'll print on.
Only your printer can really give you precise information on this.
You can always try to find an equivalent of the paper U and C versions using the Pantone converter.
It's not 100% precise but if you don't have access to any other Pantone book like the Home version or can't visit the printer, it can be useful. You need to look on the bottom page for the search results and find the one for Plastics (if your printer uses this Pantone "book"):
And another reference for cross-reference from paper to plastic (they seem to only show the coated versions):
Cross-reference for all the other Pantone:
How To Convert Pantone Tint to similar Pantone Color
How to convert Pantone 7C to TPX?
How do Pantone coated and uncoated colors relate?
Printed Uncoated PMS on Coated Stock