What he said.
I don't think any sword could destroy the One Ring. Part of the reason it could only be destroyed by the fires of Mount Doom was that was where it was created. Otherwise Frodo could have pitched into any old volcano.
If the sword in question had something to do with creating the Ring, or contained some of Sauron's power, then that sword could damage or destroy the Ring. Otherwise, I think not.
However, if we're pitting Middle Earth's warriors against wulin warriors, I think the folks of Middle Earth would be in trouble, especially the Men, Dwarves and Hobbits. The Elves, not so much. Not just because they can't die, but because they're just incredibly powerful, especially if we're talking Elves during the First Age. Feanor and his brothers would kick any martial artist's butt.