Today I started a Cuphead run with no charms, no supers, and only Peashooter (if somebody who hasn't played is reading this, then Peashooter is the starter weapon).
Isle I went down easy as pie.
Isle II is where things start to get problematic, though.
In the middle of Fiery Frolic, I realized that if I ever beat the main game like this, I can't play the DLC, because it would automatically force the Astral Cookie into my inventory, therefore ruining my proof that I didn't use any charms.