Map keys only from a specific (gaming) keyboard

I bought a mouse which has a little thumb "joystick". That joystick appears in the system as a "SOAI USB Gaming Mouse Keyboard" (the mouse part of the). When I move the stick around it acts as a keyboard typing asdw. What I want is to remap these keys to mouse movements (left, down, right, up), but only for that specific keyboard, not in general. Therefore something like https://steamcommunity.com/app/226620/discussions/0/558756255988275461/?l=russian

xmodmap -e 'keycode 25 = Up'
xmodmap -e 'keycode 38 = Left'
xmodmap -e 'keycode 39 = Down'
xmodmap -e 'keycode 40 = Right'

is not a solution, even thought it could be remapped. I'd like to use my regular keyboard while I'm using the mouse or the joystick.

I installed qjoypad but that didn't find any devices. I guess that may look for "real" joysticks? Not sure. Have anyone tried this https://bbs.archlinux.org/viewtopic.php?id=144123 or this http://manpages.ubuntu.com/manpages/trusty/man1/keynav.1.html ? I'm in the dark.

This was the closest issue I found ubuntu18.04 How to map a key to a another value but only for specific keyboard but it's still far from mine because those two keyboards are not connected at the same time.