[Inziladun]

You make a lot of sense, Gordis.
I would wonder, however, if the other Rings would have been as 'free' when Sauron was bereft of the One as the Three were.
The Three were made by Celebrimbor alone, with entirely different powers and purposes from the others. Their connection to the One was therefore weaker, but still there due to Sauron's ultimate influence in their making. For that reason, I do not think the Elves could have been reduced to wraiths in any case, merely dominated and controlled by Sauron with the One.
Any of the Seven given to a Man after the One was lost would, I think, have resulted in the possessor becoming Gollum-like. Ultimately in thrall to the Ring he bore and enduring beyond his years, but not entering the wraith-world due to the lack of Sauron's direct influence through the One.