if we are talking about a virtual machine I would simply shutdown the VM, move it to the other network, turn it on again, then access the console and re-establish networking temporarily by running
ifconfig eth 192.168.0.1 netmask 255.255.255.0 up
route add default gw 192.168.0.254
That will allow you to access the UI. Go to the UI and update the network configuration.
If this is a physical machine I would go to the UI and update the network settings. You will lose network connectivity then until you physically connect to the box to the correct network. Then it will become available again.
If you have physical access you can shutdown the hardware by accessing the console. If there is no physical connectivity I would make a one-time cronjob that shuts down the machine in the evening, update the network configuration and move the appliance once it shut down.
If you have access to the console you could also first move the hardware and then use above steps to set up networking again.
As an alternative you can configure an additional NIC with the net network details and simply use another NIC in the new location.
I'm having problems with the default gateway. I moved the appliance (a VM running MWG v22.214.171.124.0) to the new vLAN, logged in to the console to set the IP address and default gateway. Then I set the address and gateway in the UI and rebooted, but the gateway doesn't get set during the restart and the appliance ends up with no default gateway. I have to go to the console and add it using "route add..." to communicate with the server.
In the UI, I set it in Configuration->Appliances->[appliance name]->Network Interfaces. I'm using IPv4 only. Is there anywhere else I should have to set the IP address or default gateway?