As Max said, you can use the DHCP on the ZD, but running 2 DHCP instances on the same subnet will probably cause you more problems than it will solve. The ZD doesn't support DHCP on more subnets.
To put devices on another subnet and routing them correctly will require you having properly configured L3 switches. Then you will be able to put all APs and the ZD on that network and run ZDs DHCP server for everything. So if I undesrtand your situation correctly you would need to talk to you LA and get them to configure your wired network like that.