This came up in the comments to another question.
According to the LettersLetter #246 of J. R. R. Tolkien,
Sauron ... still through their nine rings (which he held) had primary control of their wills. (emphasis mine)
(The quote was copied from another question.)
So Sauron controlled the ringwraiths by having physical access to their nine rings.
If somebody stole the nine rings from Sauron, could that person control the ringwraiths?
I prefer answers based on canon sources or from letters and quotes from Tolkien.