Just tell the browser to use the wireless network somehow?
Isso pode ser de interesse:
ForceBindIP - Vincule qualquer aplicativo do Windows a uma interface específica
ForceBindIP is a freeware Windows application that will inject itself into another application and alter how certain Windows Sockets calls are made, allowing you to force the other application to use a specific network interface / IP address. This is useful if you are in an environment with multiple interfaces and your application has no such option for binding to a specific interface.