For example, I know that HDMI cables explicitly do not send a CC signal to the TV, even if the source and TV both support it.

I assume that coax cable does support it since I can use a digital antenna and receive CC on my TV from digital over the air broadcasts (in the US).

Is there any other cabling that will carry the actual CC signal for the TV to decode?

I am currently sending a DVI signal to projectors in an auditorium and I am sending the same image by VGA over CAT5 to HDTVs in our lobby. We may need to add Closed Captioning to the lobby feed only so I do not want to change the image going to the projectors in the auditorium.