Do I have to re-key the audit configurations when I am ready to transport them to Production?

No. All you need to do is use the Migrate/Copy feature to move an audit configuration from one instance to another, or from one revision to another. A valid database link must be maintained for this purpose. Alternatively, you may use AA’s Export/Import feature, which enables you to download/upload a copy of your audit configurations to/from a configuration file. Once you have copied the configuration file to a remote instance, you import it into the AA environment.  Whether you use a database link or a configuration file, you must compile the audit configurations to activate the triggers in order for them to begin creating the audit trail.