I have seen it stated that it is best to remove from network first using hassio. If you forget then most of the time a factory reset will free it. Not hard to do if you have all of the manuals / user guides.
The Z-Wave controller holds the list of devices in the mesh, and your configuration.yaml will hold your encryption key (network_key) if you set it. The file zwcfg_*.xml is a cache of names (and last seen values).
All you need to do, as others have said, is copy your config over and move the controller. The only essential thing in the config from a Z-Wave perspective is actually that network_key, if you’ve set it.
I just did something similar to this 4 weeks ago. I was running HassAIO and switched to Hassio. I just kept a copy of all my config files and dropped them into hassio. No errors and was up and running with the exact same zwave network in ~1 minute + a restart.