The OP had it right to begin with. The RS (Radio Scrambling) token stays for full effect on a turn-coat traitor. I've re-read the RS rules twice over and there's no rule allowing you to discard a traitor's RS token.
There is this "If the NORAD player switches ON a Radio Scrambler, it will scramble the Salemite player's frequencies." (p 26) But to me this is just describing the rough framework for the involved and confuseable RS rules. The rules go on in minute and structured detail describing every step of using RS. They don't give an exception for traitors and they function fine as written.
The rules are clear "...when switched on; the Radio Scrambler will scramble the Salemite's frequencies..."
Therefore if Cherokee Bill turns coat; he is no longer a "Salemite". And if he's no longer a Salemite; it means that his frequency is no longer scrambled.