IRL the Bec de corbin had a very long handle so you handle it like a staff with both hand to defend. And that long handle gave momentum to hit with either the hammer or the pick sides of the head. Head that was smaller than many believes to not make the weapon to heavy so even fat bourgeois from the town militia could handle hit without getting themselves immediately.
It isn’t absurd to make it a dexterity weapon because of this long handle and it moderate weight for its overall size.