My view is Aragorn would not use the ring from the Nazgul is because of threat of corruption. The reason why I think this is as follows...
Originally there were 19 rings (9 for men, 7 for dwarves, 3 for elves) and they were forged by the Noldor Elves under the guidance of Celebrimbor - the three elven rings were forged by Celebrimbor alone. Sadly, Sauron tricked Celebrimbor into revealing the secret of the rings. Sauron then made the One Ring in order to rule the other rings. So the One Ring has power over the other rings.
Sauron's plan was not entirely successful. Celebrimbor was able to realise Sauron's trap and free the three elven rings from Sauron's influence (arguably as he alone had made the three elvish rings). Sauron's influence could reach the Dwarves, but they turned out to be largely immune (though it gave them a lust for gold). Men, of course, were an easy target. So, the rings do corrupt even though they were not forged for that purpose but it is the One Ring.
Sauron placed much of his own essence into the One Ring, resulting in a strange link between the Ring and Sauron. While the ring exists Sauron will endure, which is how he survives the destruction of his body at the end of the Second Age. So anyone who wears the One Ring will be corrupted as so much of Sauron's essence is in the Ring. The One Ring influences the 16 rings of dwarves and men. Again, because so much of Sauron is in the Ring anyone wearing those rings will be also be corrupted through the influence of the One Ring.
What would happen if an Elf wore the one of the rings of men or dwarves is an interesting idea. On one hand Elves are meant to be uncorruptable. On the other Sauron is the ultimate corrupting force. I'd go with that the Elf would feel so uncomfortable handling one of these rings that he or she would't wear it.
The hardest question is the one about whee the rings go when a Nazgul is destroyed. Nazguls are wraiths so don't exist in the real world, but when their bodies are destroyed at the Ford of Bruinen they don't seem to lose any rings. So I guess the Ring stays with the Nazgul spirit while it finds a new body. This leads me on to my question...
Can someone tell me if the Chief Nazgul's ring is left behind after he is killed at Pelannor Fields? If it was, where does it say that in Return of the King? It could be Aragorn never put a ring on as he never got a chance to!