external vlan

I have a number of catalyst 3750 stackable switches in the network. We are on 5 floors, each floor has it's own catalyst stack which ties into the core stack on the 1st floor. We are also layer 3 ip routing capable and have a number of vlans defined. I have some requests to run some dedicated ports, on other floors, that terminate to a switch that's connected outside the firewall. I'm thinking the way i have to do this is to define a vlan on an ip range that is defined on our external static range. Then connect the ports in the other floors, to access mode configured vlan ports at the floor switches and the core switch. Then connect the core port to the external switch. If done this way, i believe i'd have to route our external public address range internally. Is there another way to do this. Thanks