The music fingerprinting on my Android phone works in airplane mode, so it would be possible with modifications. Also, it's likely that Shazam is sending a "hash" of the audio rather than an audio stream in most cases.
European law tends not to like "clever" workarounds. IANAL but I belive you would still be practicing illegal surveillance.
Its not a hash though? Its a reverse - fourier transform system that matches the sound- similar to the filter that filters out the vuvuzelas?
https://www.dechicchis.com/assets/Joseph-DeChicchis-Music-Id...
Like having a distinctive click impulse and get the cathedral from that.