If i remember correctly there is no way to pull the lightgun calibration utility directly with the menu, you need to press F10 with a keyboard and repeat the procedure for each core.
Not very practical for people like me that doesn't use a keyboard with their mister. So why not add an entry in the menu somewhere in bootup menu and in cores that support lightgun (for example under the controller key mapping).
Can you plug in a keyboard once and remap it to a button?
I don't even know how to do it. My controller is a powera fusion for switch, the only unused button is the "screenshot" button, but i have no idea how to map it to the F10 button of a keyboard.
And even then, the lightgun calibration screen is the only "hidden" menu i know of, i don't understand why there shouldn't be an entry in the menu.
Have you tried the remote app? It has a keyboard option with function keys.