Use the following string when calling your powershell script:
powershell.exe -ExecutionPolicy Bypass -File "C:\YourPathHere\Discord_QuakeSounds\Play-QuakeSounds.ps1"

Use whatever program you would like to bind the hotkey. 
There is a shortcut included which you can use to set the path, then bind with a hotkey. 

Autohotkey is another method.