Z/X/C and arrow keys is how Cave Story is controlled (and apparently a lot of other 2D platformers), and this game is partially based on Cave Story.
I'd like to add rebinds, but jam's deadline is already done, so it cannot be done right now without breaking the rules. Sorry.
(also, this "classic" paradigm only works on consoles and 3D games, in my opinion, but feel free to disagree)