Meh
Honestly, if you have serious privacy concerns and you're using a service like Shazam, you're a fool. However much they process (a handful of FFTs, I assume, with some proprietary nonsense seasoning) and encrypt the audio, you're still taking your personal audio and sending it over the Internet. The idea that such a service could be made 'safe' just creates a false sense of security. If you're worried about someone listening in, don't install software designed to listen in. Shazam probably ought to have been more upfront about how its software works, but come on - surely if you're really concerned about privacy, that takes precedence over your desire to find out what's playing on the radio?