And is about as faulty. The Witch-king would definitely have been affected after putting on the ring of power (and would have immediately killed them before returning it to Sauron). It is also worth noting that Frodo didn't have his normal nervousness about handing the ring to Bombadil.
The Witch King would immediately seize the One Ring for himself.
Although the notion of a ringwraith singing and dancing is amusing.
the first two points really don’t help the credibility of this theory. it does actually get better after that