As I believe Gwaihir was saying earlier, Glorfindel's prophecy regarding the Witch-king is "not by the hand of man will he fall". He does not say that the Witch-king cannot be killed by a man, but that this will not happen.
That being said, Gandalf is not a man: he is an angelic emissary of the Valar, of the same order of beings as Sauron himself; and his human form is as temporary as a suit of clothes. The Witch-king is a corrupted human, and therefore of a lesser order, so his chances of defeating Gandalf, whatever powers he may have been awarded by his master, are slim to none. The Nazgûl are in fact much less powerful than the films make them appear. In a letter, Tolkien wrote of them:
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Their peril is almost entirely due to the unreasoning fear which they inspire (like ghosts). They have no great physical power against the fearless; but what they have, and the fear that they inspire, is enormously increased in darkness. The Witch-king, their leader, is more powerful in all ways than the others; but he must not yet be raised to the stature of vol. III. There, put in command by Sauron, he is given an added demonic force. But even in the Battle of the Pelennor, the darkness had only just broken.
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Although Tolkien speaks of an 'added demonic force' it was clearly not enough to protect the Witch-king even from a blade made by men (even the Númenoreans were only human). Gandalf is more powerful in every way than both Merry and the makers of his barrow blade; and if it came to it, his sword, Glamdring, was made in Gondolin by the Elves, of whom the Númenoreans were only protégés. I have no doubt that Gandalf would not only have defeated the Witch-king, but done it so decisively that all drama would have been lost. Besides, he would have preferred that the races of Middle-earth dealt with the Lord of the Nazgûl themselves rather than relying on him to do it. The way in which matters transpired was truer to the Istari's mission than a direct confrontation with evil would have been.
In any case, I suspect that when Glorfindel made his prophecy on the battlefield long before he may have had an intimation of exactly how matters would turn out at the Pelennor Fields. This is why he made no mention of how the Witch-king could be defeated, or who would be able to kill him. It's quite possible that anyone could have done it, given the right weapon, but that Éowyn and Merry were destined actually to do the deed.