Cox TV is Contour 1. It's the original Contour. When Cox converted to the current Contour platform, people began referring to the previous version as Contour 1 and the new one as Contour 2. But the word "Contour" isn't found on any Cox TV screen (guide, settings, etc.). Take a look at the digital receivers page. The service type is Cox TV and/or Contour.
Yes, if OP is willing to replace his Cox TV receiver with Contour, he'll be able to schedule recordings with the app or on watchtv.cox.com. But I don't think he'll do that and if he does, he may soon regret it. I'll never willingly give up my Cox TV receiver for Contour (Contour 2).