After years of fleeing from his past, Aragorn would perhaps not only ready to face it now but also be willing to prove to himself and to all races that the race of men are mighty trustworthy, too. He may have difficult moments with the ring along the way but in the end, I feel, he would relligiously do the duty required of him and cast it into the fires of Mt. Doom cleaning once again the once tainted reputation of humans (thanks to Isildur).
Second option would be Sam. Good ol' reliable and loyal Samwise Gamgee. I don't think there should be any explanation for this. "I don't want to use it."
Then maybe Elrond, to finally let his troubled heart rest in peace.
