There are two times where Corvo doesn't use the Folding Blade; in mission 1 at the start of the game, and in mission 7 until he retrieves his equipment, which is entirely optional. You could play the entire rest of the game with a different sword, or without a sword at all.
You can pick up an Officer's Sword in either mission, if you do not pick up the first sword you come across. All other swords show up in the inventory normally, even the Gang Cleaver, which you also can only get late in mission 7.
It would be fun if future DLC would allow you to freely choose your sword, in which case this should definitely be fixed.