I looked through the game menus but the only sound options I found was to switch between mono and stereo sound. Is there a way (maybe also unconventional ways like manipulating files in the game folder, parameters to execute the game.exe with etc...) to mute the sound completely?
Well, if unconventional is okay, just open your Windows sound mixer and mute the game there. Right click your taskbar's volume icon, select open volume mixer, and click the volume icon underneath Abe's Oddysee once to mute it. To unmute, just click it again.
You can also access the mixer by pressing Win+R and then typing in
sndvol and hitting enter.