In The Fellowship of the Rings, Frodo sees the true appearance of the Nazgûl:
He was able to see beneath their black wrappings. There were five tall figures: two standing on the lip of the dell, three advancing. In their white faces burned keen and merciless eyes; under their mantles were long grey robes; upon their grey hairs were helms of silver; in their haggard hands were swords of steel. Their eyes fell on him and pierced him, as they rushed towards him.
The Fellowship of the Ring - J.R.R. Tolkien - chapter 11, A Knife In the Dark
There's no mention of the Nazgûl wearing the rings of power that Sauron gave them, although their hands are referenced. Did the Nazgûl retain their rings of power once they became wraiths? Or did something else happen to the rings once the Nazgûl emerged?¹
¹ As an FYI, I am currently re-reading The Lord of the Rings trilogy and am just pages from being done with The Fellowship of the Ring. I'm very familiar with the Peter Jackson movies. So that's where I'm coming from as far as canon knowledge goes.