Thanks for your responses, everyone. Sounds like it's a little too risky to run both versions on the same libraries, so I'm not going to try.
By the way, for those who suggested I upgrade or replace that old machine (and are probably laughing behind my back for having such an old computer
), it's not my primary or even secondary computer. I have a desktop that I use when I'm at home, and a Win 10 laptop for when I'm not. The old laptop, as obsolete as it is, still works fine for most of what I do. I only keep it around in case there's a problem with my main laptop.
I was asking about Calibre specifically because I use it not just for books, but for music and movies as well. In my opinion it's a better media organizer than any other media organizer out there, despite not being designed for that purpose. My entire movie and music collections are dependent on Calibre, and that old laptop is perfectly adequate for watching movies and listening to music.
Once I upgrade Calibre I won't run it on the old laptop anymore, which is fine. I can still access the files inside the libraries directly, as long as I'm careful not to change anything. I keep my authors and titles nice and tidy, so although it's not as convenient as going through the Calibre interface, it shouldn't be too hard to look up what I want to watch or listen to.