Is COX internet required to use apps like Netflix through the contour box?

Currently have internet, cable and phone through Cox. Going to cancel internet service over slow up speeds and data limits. 

If I cancel internet through Cox, then will I still be able to use apps like Netflix or Prime etc through the contour box? 

I can't find anywhere in settings on the contour box to input a different wireless network.

I asked (what I thought was a simple question) to a chat person. Do I have to have Cox internet to use apps on the contour box.

She suggested that I tell the smart tv about the new wifi network and the contour box would get the information from the tv because the "contour box and the tv are connected with wires."

Any opinions or insights would be greatly appreciated so I can prepare accordingly. Thanks!