When
Aragorn jumped at them, they probably didn't "see" Aragorn. They saw the burning brands. However, there is a good debate there in an old infamous
Harad thread (Called
Nazgul Incompetence or something. . .I'll try and drag it up). I think they would have noticed Aragorn was a very brave man, otherwise he would not have jumped forward at all, and they probably would have gotten the idea that he was somehow "special" for lack of a better term, but I don't think he would have gone at them with the full, "I am king, hear me roar," bit.
It is interesting to note that
Glorfindel (who we can assume was armed. . .I can't remember if it is mentioned or not) also chooses to wield burning brands at the ford, not whatever
sword he happened to have on him, and I would think Glorfindel would have been in possession of a blade at least as powerful as
Narsil. He is, after all, a very powerful and ancient
elf.
If so we can assume that Glorfindel, as well as Darling
Strider, considers blades useless against these beasties. . .or at least considers fire superior.
However, it was Glorfindel, wasn't it, who made the prophecy that a man could not kill the Nazgul. If he meant that as "man as a sex" rather than "Man as a
race" he might have thought "I can't kill this guy anyway, so I'll just frighten them with fiery sticks."