I'd suggest changing the arrow keys and backspace controls, since the player's right hand will be over the mouse instead and can be difficult to mentally swap from mouse to keyboard then back to mouse.
I think some of your movement could be based on the weapons themselves if you're not a fan of giving the player direct movement options. I'm not sure if this would wreck the balance of the game or go against your design doc, but having two guns on you at a time and swapping between them could lead to interesting movement. Something that came to mind while playing was using the shotgun to gain a lot of air, then swapping to the pistols to sustain yourself at the peak of the jump. I think a system like that could encourage players to experiment with all the weapons you add, since each combo has the potential to be really unique.
Even with more limited movement though, this is still a really fun demo, and I can't wait to see more and see how you develop the levels and mechanics.
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Thanks! Yeah, I agree with your suggestions. PC controls were a recent addition and could be improved in most areas, like menus. I do like the idea of having two guns, but I'm worried about the balance, since there are puzzles based around getting from point A to point B with limited jumps, and with two guns it may get quite complicated for me to design and the player to figure out the right combo. But maybe it'd work as a mid-game unlockable, where you'd then be able to breeze through old areas and have new, more complex areas that take two guns into account. That's something I think would be pretty good, actually.