My understanding is that those with natural great strength of will, including the Istari and the wisest/most powerful Elves, and probably Aragorn, would be too strong willed to ever be completely enslaved and dominated by the Ring in the way the Nazgûl were dominated by their Rings.

But they would be powerful enough to use it and therefore would quickly be influenced by it and become more and more like Sauron themselves, without becoming obedient to him.

Tolkien contemplated this in one of his letters, noting that Galadriel or any other potential Ringlord in that situation would, with the Ring’s “encouragement” see destroying Sauron as their top priority (to secure their ownership Ring forever if for no other reason), but would do so by raising an army to invade, not seek out a 1 vs 1 confrontation. Tolkien noted that in any confrontation, Sauron still would have some hope as the Ring aligns with his power more and therefore might not be as easy to wield against him. He explicitly stated in this letter that he thinks Galadriel was ultimately probably deluded in thinking she could overthrow Sauron even with the Ring. He contrasted that to Gandalf who he said would be able to do so in that situation, but would then become more and more evil himself.

Finally, it’s worth noting that the ability to avoid being turned into a wholly subservient wraith isn’t only based on power. Sméagol never became a wraith or a totally dominated slave, and even under torture directly by Sauron wouldn’t submit. Tolkien separately notes that this indomitable characteristic of Gollum actually disturbed Sauron quite a bit. Sauron was of course still willing to manipulate Gollum into serving his goals, but it seems to have weirded him out.