Depends on which sticks you have. If they support it, you can use the NVM backup and restore functionality provided by zwavejs2mqtt to move the network from one stick to another. In that case, you don’t need to exclude and re-include anything.
Stock Nortek and Aeotec Gen 5 < v1.2 sticks don’t support this functionality.
If your source and target controllers are the exact same device, then you can use any tool to do a backup and restore: zwavejs2mqtt, Silicon Labs PC-Controller software, or the Z-Wave.me Z-Way software.
What’s the purpose of removing and re-adding devices? Just plug your original stick into your new HA setup.