This is way too limiting, even if thematic. I have a small suggestion about how this could be changed to embrace a little more:
Allows the Arbalest to equip any Sword, Axe or Spear as a sub-weapon. When a weapon of one of those types (or any type, if monoclassing) is equipped as a sub-weapon, it is fired when using Cannon Skills. (If Arbalest is your main class, any melee weapon that is not listed above can also be used as armament, but it increases the cooldown by 2.)
See Arbalest Cannon for more details.