I'd imagine that each crafting discipline is responsible for making different parts of the airship. With the Ixali quests, all classes were allowed to make the same recipes, but that was more for convenience' sake. The way I picture it:

Armorer: Exterior Hull
Carpenter: Interior Hull, Masts
Blacksmith: Weapons
Goldsmith: Ship's Instruments
Alchemist: Fuel, Black Powder
Leatherworker: Sails and Rigging
Weaver: Team Jackets
Culinarian: Dat Grog

And I foresee that there will be a huge collective grind to make your airship not only crafting-wise but gathering as well. You might need 10,000 Spruce Lumber just to build your hull! Miners could collect materials for fuel and maybe Fish could get involved somehow.

They will likely add another door in our FC house basements that leads to our workshop along with a crystal that takes us directly to the airship dock in Heavensward's new Sky areas; that means no airships floating around in the Mist!