Normally I am against lens snobbery, but the Nikon 80-200/4.5-5.6 AF is one of the cheapest humblest lenses they marketed or made. That doesn't mean it's bad, I just wouldn't spend a lot of effort on thinking about which one to fix. Whatever is the least effort. If you swap the lens mounts and it's not much effort, if the one with broken lens mount turns out to be misaligned and make bad images, swap the mounts back.
It is a completely different lens from the older 80-200/4.5 manual focus lens (which is a pretty good lens, but never came in an AF version), so experience with that doesn't carry over.
Working on zoom lenses can be difficult. I repaired one Nikon 70-210/4-5.6 AF (slow, but not a bad lens), but tore the flex connector for the AF/electronic contacts, so it wouldn't AF or communicate electronically. Eventually, IIRC, I got another one that had some problem with the AF screwdriver and was able to combine parts to make them into one working AF and one MF lens.