If you're discovering the controller via DHCP, that's the critical change for you (where APs are on different subnets to the controller IPs).
I.e. I would...
1. Create your new IP interface and VLAN on the controller (the new MGMT)
2. Then change your DHCP option settings (if these point at an old address you intend to remove), and test discovery (reboot some APs)
3. Then set the LMS as you desire in the system profiles moving forward (as CJ says, this only affects AP homing AFTER discovery), and test APs attach to the intended controller
4. Remove any legacy IP/VLAN config when you know you're not using it.
This way, you should be able to back out any step if you hit a problem.