Custom content on a specific page on a specific blog in multisite

I have one blog (among a growing collection) to which I would like to add some custom pages. So far, so easy. However, these pages would run the UI (form) of custom PHP and JQuery. This should only be available to that one blog site and that one page and be impossible for any other blog to even know about, let alone use or embed. Furthermore, the content cannot show up or impact the other sites at all – even if I screw up and write very bad code.

For this reason, I have ruled out using a plugin (which would have my code show up in the plugins list on every site). For the same reason, I cannot see that adding a child theme would work as then I would have two identical themes for all the other sites and one would have some funky extra stuff that the other admins should leave alone if they know what’s good for them.

I’m stuck. How do I do this?