It is possible to allow the Customizer to use more than one changeset. The default is not that, though, so you have to research how to do the “branch” method of changesets.
You can’t remove the uuid in the query string, or the Customizer won’t know which changeset to load.
With the default, you can save one changeset as draft and send that URL to someone. They will see the site with those options even if not logged in. That means you can put that link on your page and it would work. But only one draft is managed by default, and I think it has an expiration.
The Customizer changeset is a custom post type, saved in the posts table.
example:
