In order to be eligible to get the transmog version (Arsenal: The Warglaives of Azzinoth), you MUST first have the Feat of Strength achievement (Warglaives of Azzinoth) from equipping both Warglaives of Azzinoth on the same character.
Then any character on that same Battle Net account can kill Illidan in the BC Timewalking version of the Black Temple and unlock the transmog for their Demon Hunter.
More info here: https://www.wowhead.com/black-temple-timewalking-loot-transmogrification-guide#warglaive-transmogrification