If I wanted to make a game based solely on keyboard input with no mouse cursor, would the best way to achieve this be to set the cursor mode to 'wait' and give it a transparent graphic?
Why not HideMouseCursor()?
Would this also completely disable it's use?
Nope, but all mouse usage were designed by the game maker him(her)self, so you can just don't use any interactions related to mouse usage in your game (and comment out any mouse-related stuff in the script).
Or, if you want to use these interactions, you could combine HideMouseCursor() with your idea of setting a mouse cursor to the wait mode. Thus, only the any click interaction is possible for player to run with a mouse click but you can then just don't use it at all.
Or you could just take the on_mouse_click function and have it simply read 'return'.