I don't know whether Hollow Knight uses an input library (like SDL) that would allow controller tweaks, but it might be worth investigating.
Steam generally gets games with poor/rigid controller support to work via Steam Input, which creates a virtual device that behaves like an Xbox controller and maps the real controller's inputs to it. You're not using Steam, but this project does the same sort of thing, and might be helpful:
https://github.com/chrippa/ds4drv
I don't know if it's still maintained, but if it chokes on a new distro, one if its forks might work.