Ex Shazam tech here. The signatures that the Shazam app sends are very small, so bandwith costs should be minimal. Of course, I speaking about the technology of my day 2001+, so times may have changed

Some phone plans like Google Fi will give you a data only sim card for free. It ends up being totally free as long as you have unlimited data plans. I use my old phone and a data only sim card for random projects.

I did some measurements on shazam and it seems to send about 7kb/minute, which corresponds to 300MB/month, i.e. no big deal. I suppose it helps that shazam was designed in the age of expensive bandwidth.

I've learned when setting up a family plan that depending on how many devices you already have (my wife and I each had 1 phone and 1 apple watch) we could get an extra line with unlimited data for functionally nothing. (The sim's sitting in my dashcam right now, been silently plugging away for months)