We may think picking a different menu from the back end is simple enough, but it could be hopelessly confusing for some end users. If you think there’s a need for an even easier UI, the menu used can be altered through the “wp_nav_menu_args” filter. The chosen menu could be stored in an option value and filter code assigns the option value to the “menu” arg.

Many themes have more than one menu location, be sure you’re changing the right one. You could even code it so the menu used is determined by the current date. Just don’t hardcode the date criteria. They ought to be editable through an UI somewhere.

Creating a good UI can get pretty involved. You may want to revisit how we would normally switch between menus in the back end as it is now. I’m not a good judge of such things, but I don’t see it as being all that difficult. It may be confusing at first, but it’ll get easier with practice. The existing UI is a lot easier to use than the effort of coding up a new one would be.