You should already be using unicast over MGMT interface as backup. Place the standby unit into inactive mode to be sure of no failover events. Make sure you have connectivity between self IPs created on the new VLAN, and then change the ConfigSync, Network Failover, and Mirroring IP addresses to use the new VLAN self IPs. Remember port lockdown should be 'default'.
If you want step by step... thats professional services. We dont write Methods of Procedure or Change Request procedures here 😉 Hope this helps to give you enough information though to complete that work yourself. Good luck!