It sounds like you do want a custom post type, you just want to set the public argument to false. The register_post_type() has lots of arguments that will let you do everything you probably want. Along with public, you’ll probably set has_archive to false. Setting show_ui to true will allow you to manage the posts in the backend.
If you want to group the “fast facts” in any way, register a taxonomy to go along with your post type.
Obviously, you’ll still have to fill in some blanks and write a widget to put into the sidebar, but I think this answers your main question.