Is it possible to disable the ability to check multiple categories for an entry in the control panel, only leaving the option to check one category?
If I actually understand you question, no, it's not possible with native EE. You would need to write a custom add-on. However, with something like this:
You can can probably add both of those categories as Primary Categories; and only one should be selectable. It probably isn't exactly what you want, but I'm not sure. Check out the docs (or just download it and test it on a dev server, it's free anyways) and see if this is right for you.