Speculations and another 'what if' scenario

[Rumil]

I believe the answer to this is in Unfinished Tales, in the chapter on the hunt for the ring. Haven't got UT to hand at the moment, but it says that the Nazgul were the only servants that Sauron could trust to bring the ring back to him as he completely dominated them. I'm not totally convinced (either way) but many have said that Sauron actually held the nine rings, rather than the Nazgul wearing them, presumably that means he had them by the short and curlies (or undead equivalent!).

Interestingly, in one version of the hunt for the ring, the Nazgul stop off to question Saruman at Isengard. Saruman denies that he has the ring and claims that otherwise the Nazgul would serve him. Therefore if one of the 'wise' had succumbed to the power of the ring, the Nazgul would likely be under their command.