Remap mouse buttons

Problem

Is there a way to remap mouse buttons M4 and M5 (forward and backward)? In particular, I would like to move across workspaces with

ctrl - M4 : skhd -k "ctrl - left"
ctrl - M5 : skhd -k "ctrl - right"

I could not find the keycodes for any mouse button, and it seems that mices do not actually send normal keyboard strokes. Are they implemented in skhd? In case, there is no mention in #1.