In the bio3.ini (located in the install directory) there's this section:

[Keyboard]
Key1=200,72
Key2=208,80
Key3=203,75
Key4=205,77
Key5=
Key6=47
Key7=50
Key8=48
Key9=31
KeyA=45
KeyB=16
KeyC=44
KeyD=57,46,28
KeyE=

with the numbers obviously referring to specific keys on the keyboard.

Anyone happen to know where one could look up what numbers equal which keys specifically? A list or something?

Use the F1 key to bring up the option menu. Use right click to open the menu and rebind the keys.
But be aware that changing the resolution can cause your game to crash.

Nevermind, figured it out.

- bring up the in-game configuration by pressing F1
- go to the Keyboard settings
- right-click on the entry you want to rebind, a menu will appear with the options "Add key", "Clear" and "Set default"
- the rest should be self-explanatory

Mouse buttons are not recognised, unfortunately.
Should be able to work around that with a AutoHotkey script. As stated, figured it out by myself.
Thanks anyway.