Tom,
As Dropbox is the storage channel for the music, all you would need to do is ensure the music folder(s) storing your music have the selective sync set to "Local" (instead of online-only). If you want to then move the music from Dropbox to another location, you can do that by right-clicking (sorry, I don't have my Pro plan on this machine so I can't give you the exact thing to click on), and select "remove from cloud" -- this is provided the music started in a folder outside of Dropbox. If you put the music into Dropbox and then imported to rekordbox, it would require that you manually move it to another local folder.
If you're going to do that, I would recommend disabling the cloud sync before you move the files, or the other computer will also think you've removed them.