How to disable cache for the content returned by a shortcode

As the caching usually doesn’t work on parts of the page, but on the whole page, you can’t have it just not cache that specific part (well, you could use ESI/Edge Side Includes, but that’s not an option for all implementations).

What you could to is write a hook that checks whether these shortcodes are used and adjust headers indicating that it might not be cached or only cached up to X seconds (with the indicated max lifetime falling on the date and time you want to show the changed content).

Or you could parse the shortcodes when posts are updated and add WP cronjobs that will silently update the post. You’ll most likely have some sort of purging mechanism in your cache implementation that removes the cached result if the post is updated.