Since you can't change the controls in-game, why not try an out-of-game remapper? I don't use Windows myself, so I don't really know what's popular or what works, but a brief Google search turned up AutoHotkey, which is fully free software and mostly appears to be able to do at least the key remapping. It supports joysticks, but it still passes through joystick events, so the game's default bindings might get in the way.
https://autohotkey.com/
As to the joystick config, there are several commonly mentioned joystick-to-keyboard mappers out there, but I just gloss over such posts and can't tell you an exact name.
I tried autohotkey myself, and wrote a q&d arrows -> wasd config to see if it works, and holy crap, it actually works in Wine. Can't be sure if it works in Windows, though.
#IfWinActive Cosmic Star Heroine
*w::Send {Up Down}
*w Up::Send {Up Up}
*a::Send {Left Down}
*a Up::Send {Left Up}
*s::Send {Down Down}
*s Up::Send {Down Up}
*d::Send {Right Down}
*d Up::Send {Right Up}