You have a cable box and TV capable of HD, do you really want to inject an SD device into the mix? You would have to connect the cable box to the VCR and the VCR to the TV with, at best, composite video (yellow-red-white) or coax. I'm not sure if Cox STB's will output both hdmi and coax video if you connect both, never tired it. As a test, you can try these two connections:
STB ---hdmi---> TV
STB ---coax---> VCR ---coax---> TV
then use the TV to switch inputs between hdmi and coax. Don't forget, the VCR must be set at whatever channel the STD outputs (3 or 4) and the TV must be set to the VCR output channel to use that setup. Don't forget, this is a test, I don't know if the STB will output both hdmi and coax. Good luck.