Linksys routers have the ability to switch between gateway and router configurations. This would be a solution.

Most routers function as gateways or transition points between the extenal network (internet) and internal network. Most routers direct traffic on the internal network. A lot of routers are actually gateways and don't function too well when nothing is plugged into their wan port.

The best idea is too get a wap or switch. The second router is overkill and can cause more headaches than anything else.

Good luck