Is there anyway to remap the key bindings to a mouse button? Even in the conrols_setup_default_keyboard script, it seems that there is no way to change any of those inputs to a mouse button press constant.
Nothing built-in, sadly. The approach I'd recommend (which is from a more recent project) would probably be turning keys into device/ID pairs like this...
..and then in input_get, have a switch statement that reads the appropriate device based on the first member, using the second as an ID:
(Note that the code above uses a bunch of GMS2-isms and will not work in the GMS1 version of the engine)