Aragorn gives them the swords at Bree, probably prepared for the fact that hobbits probably wouldn't have swords.
I remember that scene as well; but given the previous posters seemingly total non-awareness of it I have to ask:
Was that in the theatrical release or the extended cut? I haven't watched the theatrical release in so long I can't recall exactly what all got added.
However, that really makes no sense, as Eowyn was able to kill him with plain old iron (and a little bit of destiny), no special Numenorean magic required.
One line of argument is that Merry's stab breaks the enchantment making the Witchking vulnerable to Eowyn's attack.
Whether Eowyn+Merry actually killed it outright is a separate question; I expect it was probably just banished again, and it would have reformed. The destruction of the one ring, would have been their final demise, its destruction caused the other rings power to fail as well. The wraiths, of course, were sustained by their rings of power; the 9 rings that went to men.