You are incorrect, it indeed must be a melee weapon.
One-handed and two-handed weapons can never be anything except melee weapons. They are designations not merely of how many hands you need to use, but actual weapon categories. Bayonet yes, firearms no.When wielding a one-handed weapon in two hands or a two-handed weapon, the weapon is treated as a light shield for the purposes of performing a shield bash attack on an opponent.