Hi Brig,
It is as simple as that. There are several ways to do this. Here what I would do for the least amount of down time:
1. Change IP of one of your ZDs to be in the VLAN 10 IP Scheme
2. Change your untagged (native) VLAN on your switches from VLAN 1 to VLAN 10 for all your WAPs and both controllers
3. Change all your WAP IPs
4, Change the IP of the second ZD 1200
That should allow your network to be up and running the whole time with minimal downtime. As a note, The controllers and WAPs don't necessarily need to know that anything changed as far as the VLAN, so don't change your management VLAN in the ZDs.
Cheers,
Alex