If you are currently using the core Z-Wave JS add-on, you can follow the migration guide, but instead of using the add-on you’d be using your own installation via Docker. https://zwave-js.github.io/zwave-js-ui/#/getting-started/docker
The export and import of the existing Z-Wave JS driver cache would be the same, as well as the re-configuration of the integration (pointing to your Docker installation URL, instead of the add-on). Those are the important steps for preserving your existing configuration.
If you are currently using the community Z-Wave JS UI add-on, you can simply use the Backup and Restore functionality on the Store page.