Install new database then import records from old databases.
The import process can be scripted. "rehearse" the update using a back up copy before doing it with the current copy. The script can import from each table in turn and also can reset "next serial value" settings on any auto-entered serial numbers.
With work, this can be automated to the point where a user clicks a button, uses the dialog that opens to select the original file and then the script takes it from there to import all the data from the old into the new.
For future development work, you might research data separation as a way to reduce the amount of importing needed when deploying an update.
For larger solutions or if you have to update frequently with various changes, I recommend using Goya RefreshFM which automates the most time consuming parts to the process.