Menu custom link using shortcode?

I have a shortcode I need to use to create a link with some parameters specific to the user logged in (or not logged in) to forward to an external site.

When I enter the shortcode into the custom menu item in my theme appearance settings, it always removes the shortcode’s brackets and tries to add “https://” to the beginning of the string. So that does not work. I’d like to add the shortcode there and have it resolve in the menu when the page loads.

Is there a plugin I can do this with or otherwise a redirect scheme? I tried one redirect plugin but again, it did not recognize the shortcode and parse it.