Assuming that someone does all that, do the spar and duel options disappear if you don't have a sword in your inventory? Or does the game create one, like when you first start King Paddle? I've never had an issue with my hero specific actions not showing up personally, but I just wondered.
Edit: I don't think you can actually sell an equipped item, and the only way I can see to unequip an item is to equip something else, hence no chance for a fighting sim to be without a sword.