You can’t do it with keyboard shortcuts as it is not a menu item.
I want to this as I have assigned the other align commands to my WACOM buttons:
I made a complex keyboard shortcut for each of the commands in Illustrator (so I don’t press it accidentally). Then using the WACOM sys pref pane I then just assigned that complex button press to the key that I want. Using different combinations of modifiers I can assign all the keys and select different things using SHIFT.
But I can’t do this with the highlighted items as they don’t appear in the Keyboard Shortcuts menu. I don’t like having to open up that little tag every time I want to change the mode.
Key objects are designated by an extra click.
Select a bunch of object, then click one more time on the object you want as the key object. The key object will get a thicker highlight on it. This sets that object as the key. There’s no need to use the panels. Then align.
There is no way to have a button implement the key object (or any align function) because Illustrator needs to know which object you are referring to. It would be nice to be able to toggle those options with a button, shortcut or single click, but it’s currently not possible.
The Only way I think you could implement what you are referring to is via actions that are set specifically to use the artboard or selection.