Title tells most from the request.

Basically, instead of going through menus and file "save as" options, set how you want to export "Chord Track" in Option once. And have a nice little button in custom menu to export only Midi Chord track (no other tracks) in single click. Press the button, just point to where you want the saved file to go> name it > done.

P.S. To get a little creative, file can also get auto-generated default name of the project with words Chord_Track added to the name.