Using Dropbox to sync Local sites between computers under Local Classic

That might work, but there’s enough little things that could go wrong that you’d want to really make sure that:

  1. Your backups have been made (it sounds like that’s the case because you have the site zip)
  2. I’d probably add a “stop site” step as well as “delete site” from the Local UI. That will ensure that Local server processes have stopped, and Local won’t know about the original site.

From there, you’d essentially be creating a “new site” and so that should work.