I think I noticed something...

Black Cleaver is indeed Noxian, but no Sion and Darius wield axes that are different from the Cleaver. The main tell is that our resident axe wielding Noxians use one sided axes where as the Black Cleaver is double sided, as well as the Cleaver not having a skull on it from what we can see, where as Sion and Darius both have a skull emblem where the blade connects to the handle of the axe.

As a note, Sion and Darius have both held the same positions, that being "the Hand of Noxus"; Sion was that to Boram while Darius is that to Swain, so if we look at it, Sion's axe and armour is an older, less refined version of Darius's gear.