As I understand it (correct me if this is wrong) swords not crafted by elves are destroyed upon striking a Nazgûl- but do they do any damage to him (it?) in the process?
At least one sword, made by Men, was able to hurt the Nazgûl:
ROTK, Book V, Ch. 6 The Battle of the Pelennor Fields:
And still Meriadoc the hobbit stood there blinking through his tears, and no one spoke to him, indeed none seemed to heed him. He brushed away the tears, and stooped to pick up the green shield that Éowyn had given him, and he slung it at his back. Then he looked for his sword that he had let fall; for even as he struck his blow his arm was numbed, and now he could only use his left hand. And behold! there lay his weapon, but the blade was smoking like a dry branch that has been thrust in a fire; and as he watched it, it writhed and withered and was consumed.
So passed the sword of the Barrow-downs, work of Westernesse. But glad would he have been to know its fate who wrought it slowly long ago in the North-kingdom when the Dúnedain were young, and chief among their foes was the dread realm of Angmar and its sorcerer king. No other blade, not though mightier hands had wielded it, would have dealt that foe a wound so bitter, cleaving the undead flesh, breaking the spell that knit his unseen sinews to his will.
I will correct you:
"Look!" he cried; and stooping he lifted from the ground a black cloak that had lain there hidden by the darkness. A foot above the lower hem there was a slash. "This was the stroke of Frodo's sword," he said. "The only hurt that it did to his enemy, I fear; for it is unharmed, for all blades perish that pierce that dreadful King. More deadly to him was the name of Elbereth." - Aragorn, "Flight to the Ford," Fellowship of the Ring, p.201
It is unclear if "that dreadful king" is limited to the Witch King or the Nazgûl more generally (who had all been, at least, Lords in life).
Notwithstanding, there is no indication that:
- Only elven blades can wound Nazgûl; Frodo's blade, like Merry's subsequently, was a product of Westernesse (either in Númenor or in exile is not revealed). In addition, there is no hint that Eowyn's blade, which I recall caused some inconvenience to the Witch King, was anything other then the product of Rohan.
- That elven blades would survive; Aragorn is quite clear: "... all blades perish ...".
I think that there seem to be instances where it appears the Nazgul can be hurt by ordinary weapons. There is a passage concerning a Dunedan, "Boromir was a great captain and even the Witch-king feared him." [Appendix A: The Stewards] Why the fear? There is also another passage in which he no longer takes heed of missiles. If they could not hurt him, why does the WK heed them in the first place?
"Over the hills of slain a hideous shape appeared: a horseman, tall, hooded, cloaked in black. Slowly, trampling the fallen, he rode forth, heeding no longer any dart. He halted and held up a long pale sword. And as he did so a great fear fell upon all, defender and foe alike; and the hands of men dropped to their sides, and no bows sang. For a moment all was still."
There is also an instance during the Battle of Pelennor where he was pierced by Merry's blade, the one Tom Bombadil got for him at the Barrow-downs.
Merry's sword had stabbed him from behind, shearing through the black mantle, and passing up beneath the hauberk has pierced the sinew behind his mighty knee. [Battle of the Pelennor Fields]
A little while later in the narrative a brief history of the sword is given:
So passed the sword of the Barrow-downs, work of Westernesse. But glad would he have been to know its fate who wrought it slowly long ago in the North-kingdom when the Dúnedain were young, and chief among their foes was the dread realm of Angmar and its sorcerer king. [Battle of the Pelennor Fields]
Here there is a blade that was made slowly in the kingdom of Arnor for dealing with their enemy from Angmar. Many years later it is taken from the Barrow-downs and it does damage to the Witch-king. There is also Éowyn's sword not made by the Dúnedain;
she drove her sword between crown and mantle, as the great shoulders bowed before her. The sword broke sparkling into many shards. The crown rolled away with a clang. Éowyn fell forward upon her fallen foe. But lo! the mantle and hauberk were empty. [Battle of the Pelennor Fields]