Basically every word is open to interpretation:
The "he" might be Rand or another man (especially considering that Rand has only one hand). The "he" might be part of "the three" (which might be persons or things), or separated from them. The blade of light might be e.g. Callandor, Justice or even the dull dagger. We also don't know, if the three become one, because he holds the blade in his hands. The Prophecy doesn't really imply such a conditional, but just that the three shall be one, when he holds the blade.

In any case, nothing really suggests yet that this Prophecy is the ultimate key to win TG, or that it deals with Rand's confrontation with the DO (we know other Prophecies, which clearly refer to the end, namely Rand spilling his blood in the Pit of Doom, etc.). Apparently Min just randomly chose this one Prophecy among all Prophecies in the book. Considering that the Prophecies are likely chronologically arrayed from Rand's birth till his "death" in the Pit (at least as far as it is possibly), one would think that Min had mentioned if this Prophecy is rather tied to the very end.

In my view, this Prophecy might be related to Rand being on the boat with his three women, which Nicola (she even also mentions "a blade" in her Foretelling) and the Wise Ones foretold (and in extension with his funeral). Apparently this is a very important scene, but till now we never heard about it in the Prophecies of the Dragon, IIRC. Something will happen between Rand and his three girls, maybe it is in someway also related to LTT's "one", namely Ilyena.

But I also like the interpretation that the three ta'veren will have to unite in a special way.

Guess we will see...