It is possible to watch cable TV without a Contour box, but you can't just run the cable directly to your TV. At a minimum, you must have a mini box between the incoming cable and your TV to convert the digital signal.
Thanks CurtB. So I'm trying to avoid having to use 2 remotes (this is for my 84 year old mom) and frankly the interface on the Smart TV is so much more intuitive and easy to use so looking for a solution where the channels will be right there on the TV's homescreen next Netflix and all that other good stuff.
I haven't seen the home screen of my TV in ages. OP has a good point. It'd be nice if remotes had a button to switch to the actual TV (OS) and not just what's connected to the TV, such as tapping the HDMI Input button of the Contour remote.
However, if you want to switch devices with the Contour remote, you have to use its HDMI Input button. Perhaps connect an even simpler "home screen" to the TV. Roku has a extremely simple interface.
As far as watching cable-TV without a Contour box, the answer is no because, as with all providers, Cox encrypts its programming, so you need to rent a Cox box to decrypt the programming.