Weapons of Sharpness and Magic Weapons

[Endoperez]

That's my quess as well. However, all the attacks that don't count in ambidexterity (including Chi Boots and Gore from the helmet) could be distinguished from the normal attacks. Other than that and whether the weapon is ranged or not, weapons are just weapons. Whether unit has a weapon named "Jotun sword" or "Ice Sword", it is just a name and bunch of statistics. IIRC, the Eternal Guards mercenary group members wield Flambeaus without even the commander having the item, and some Machaka units and commander wield Bane Blades.