So I finally got time to look at this and a shortcut just to launch the extension is dead simple using built-in WebExtensions features. This has the double benefit of allowing users to change the shortcut themselves without building a shortcut editor.
Using WebExtensions commands for each of the individual options ("Clip simplified page", "Clip full page", "Clip screenshot", etc) would also be doable if a bit more work to make sure we launch the extension first as the first step. Again, it looks like we could define the shortcuts and use native browser utilities to override them.
I also tested out the Evernote extension that you referenced and that looks like a bit more work to mimic. They've got an interesting little preview overlay and the way they've implemented the shortcuts really shouldn't be done without a way to edit/turn them off imo. It might be nice to have, but I'm not sure if it's worth the investment given this thread: