Geoff,
To migrate a network from one class to another in ZERO download, would require you to setup the second network that everyone will eventually be migrating on, enable routing between the two networks (e.g install a server/router that can talk to both networks and route packets) and then start to slowly migrate the workstations and use Dynamic NAT with PAT (NAT OVERLOAD) in order to ensure they are able to access the servers on the old network.
Once the above step is complete, you can then migrate the servers on the new network, but depending on the complexity of your network and its current setup, it would require you to have a small or even none at all downtime.
Your question is the type that cannot be answered in one page. You need to create a plan for it and outline each step required in order to keep everything under control and minimise problems that might/will occur.
Cheers,
