Map a shortcut key(s) to the apple menu...?

No, not just the Command (⌘) key as it's (pardon the pun) a key element in so many system and application menus and operations. You might be able to program a ⌘+F1 key combination (or other key) to do what you want. Or just the F1 key.

Here's some food for thought: I don't use Shortcuts but use a macro app: Keyboard Maestro. With it I can do almost anything like change Safari's Advanced settings with a simple 2 key combination:

There are other macro apps at the App Store, some may have demo versions you can try. Just search for "macro". KM one of the more powerful apps available.