That particular episode originally aired on October 30th, 1963, smack in the middle of SWL/amateur radio popularity, so it's entirely possible it's either. Can you get a screen shot?
As for CB, it was around, but to my understanding, it was more of a lite-version commercial and personal service, not the "smokey and the bandit" popularity it achieved in the early-to-mid 70s. I don't think it would have offered a teenager much at the time, but I could be wrong.