"surely if you're really concerned about privacy, that takes precedence over your desire to find out what's playing on the radio?"
well, might be easier to:
a) look on the 'what is playing' section of the station's web page [a lot of them do this]
b) if it's internet streaming radio, you'll see the ID text displayed [probably]
c) who really cares, since RIAA only excretes CRAP these days, with rare exceptions
and anyway, Shazam probably wouldn't recognize anything _I_ listen to, from JPop to old jazz. Except, maybe, for decent 'more modern' stuff like Muse or Metallica.