Beastmaster's weapon?

[Nestama]

NPCs aren't a good guide though as they often throw the Armoury System to the wind, dual wielding different weapon types in ways players have never been allowed to do.

Besides, weapon is technically irrelevant anyway if BLU is anything to go by - sure it has a weapon, but that weapon's 'type' is basically just copied from an existing class (let's face it, BLU's weapon is just THM/BLM's wands given a touchup), and had no bearing on the class's gameplay at all (it was only there as a requirement of the Armoury System to actually work, needing something to be equipped in the weapon slot at all times).

I mean, even now there's only a handful of BLU weapons available even now and they're just basically glamour anyway. I see no reason to believe BST will be anything different.

Well until we see otherwise, it's still fair to assume BST will use an axe and shield (I don't think we've really seen human NPC's mix and match weapons and shields outside of GLA/PLD, THM/BLM and CNJ/WHM). Though if SE decide to go the Tactics Ogre / Battle route, then they could give them a whip (Lyon's portrait has him holding a whip. Ganpp seems more proficient with the axe than the whip, though).