For one thing "Prophecies" in Tolkien's work aren't the "Nostradamus" kind of prophecies that we are used to, it's not a fortune teller saying "you'll meet a tall dark witch-king and end him". Neither is it a fairy tale curse or enchantment Before your 16th summer you shall prick your finger . . . there by forcing fates hand.
These are not a Tolkien prophesy.
Tolkien was more of a "fate" guy, for example when the elves gave chase to Morgoth after the kinslaying they were given the Doom of Mandos. That isn't "a punishment" but lays out the consequences foreseen by those who can see further and more clearly the effects of a given action. If you do this, then this will be your fate.
Glorfindels words that became "The Witch-king prophesy" are . . .
He will not return to this land. Far off yet is his doom, and not by
the hand of man will he fall.
... and were spoken to Eärnur, a "man" ergo, non elf. So Glorfindel may have been saying "This foe is beyond your powers, it would take an Elven Lord (like me) to bring him down, and I can't see myself taking him on anytime soon".
On the other hand, it may have been Glorfindel getting a sense of the Witch-king's doom, he may have felt that it wasn't a man who would kill him.
Also the magic that protected the Witch-king wasn't specific to "men" (i.e. this shield does a quick chromosomal check of the attacker and just deflects blows from people with Y chromosome). The magical protection was magical and protected him against all blows.
However while Eowyn landed the fatal blow, it only succeeded because Merry's first blow unwound the Witch-king's magic defenses.
To answer the question
But what if instead of Eowyn, it was a Man like say Aragon or Eomer
who delivered the fatal blow to the Witch-king with their sword? Would
the prophecy hold true and the Witch-king NOT die?
If it had been Aragon or Eomer who landed the blow after Merry disabled the Witch-king's shields (as it were), then the Witch-king would have died, and proven the "prophecy" false, however that didn't happen. Could it have happened? Let's let Morpheus answer that
No, what happened, happened and couldn't have happened any other way.