Wonder why they made it a hat instead of a gun. Or even better, design your own gun.

It's because hats are sexy and everyone wants them

francis, if it's a hat, that means they can also grab things and use gun-type objects like the grappling hook or paintinator

Uh no. You can only use one power-up at a time. The hat works the same way as the paintinator. Also, the grappling hook isn't really a gun-type object. You don't aim it, but instead it grabs on to the nearest thing.
Actually I think you can sort of aim the general direction with the left stick, but you can't just go shooting it in any direction.