Best way to securely connect 2 offices in the same building for file sharing.

I need to connect two private companies located 100 feet apart in the same building. Each company has its own Internet, dhcp, dns, domain, etc. The companies want to be secure from one another as much as possible. They want to share large files at high speed so Internet is not an option. They do not want to do sneakernet. Basically it boils down to doing what firewalls do over the Internet everyday, but with a CAT6 cable between firewalls instead of an Internet connection.

I am considering the following but I'm not sure. HELP!!!!

1. Purchase 2 linksys firewall/router w/dmz
2. Run a single CAT6 drop between offices and connect to the WAN ports between the firewalls.
3. Connect LAN port of each firewall to a switch on the respective LAN
4. Connect one workstation with a share to the DMZ port of each firewall
5. Configure user workstations to route traffic destined for the other network to their linksys firewall rather than their Internet router/ default gateway.
6. Linksys has a default gateway/route which points to the WAN IP of the other Linksys.
7. Other linksys sends traffic to the network share on the DMZ.

Is this a valid config? Can both WAN ports be on the same subnet or not? Can I do it without a third router? Any ideas? thanks!