Which databases are you using? Some (postgres, for example), have the ability to create functions to query other databases directly from within them. Knowing the specific database vendors might be useful.

That said, I would think a simple dump from one database and restore to the other would be fairly quick. If you absolutely cannot tolerate any downtime (likely to be seconds only), you could try dumping and then restoring to a set of tables different from your production tables and, when the whole process is complete, simply drop the old versions and rename the new versions. Again, the details of these actions and whether they are feasible will depend on your vendors.