I just ran across this topic which addresses your issue:
osx - How to send a menubar app (with no menubar menu items) a command in AppleScript? - Stack Overflow
I don't know if you are the OP or not, and I have NOT tested the suggested solution. But maybe it will at least get you started.
This is very easy in KM, just use the
- Activate a Specific Application action (KM Wiki)
- Type a Keystroke action (KM Wiki) to issue the shortcut key.
Another option is to use the Select or Show a Menu Item action (KM Wiki), but I'm not sure if it will work in this situation.