Public site that is not listed

I want to create a site that is public but does not show up in my List of Sites page, Landing Page.
I want to use this “public” but hidden site so I can use the links from it in our institutional repository so it would show up in the institutional repository when the page loaded.
I am planning on using the Bookshelf theme and for the material to show up as a flipbook on the institutional repository page when opened.

I am open to other ideas if anyone has a suggestion.