Software engineer, I work with, says that Fourier analysis of such size files will take forever. He participates in SETI program and does analysis of small files on his computer. Ideal would be small crude scanner program that looks for high amplitudes above 2kHz.
Kijanki -- Although as you realize there is a learning curve and familiarization process involved in using an audio editing program, once you attained sufficient familiarization, doing what you describe would be trivially easy with Sound Forge (and possibly with the less expensive or free audio editing programs as well).
All you would have to do is to spend a few minutes setting up a preset in its equalizer function, that would sharply roll off everything below 2kHz, and then set up a preset in its "find" function to find everything above an amplitude that you specify.
Once you had those presets in place, you would copy the file you wanted to check to a separate folder, and open the copy with Sound Forge (that avoids the risk of accidentally modifying your original). Then all it would take would be a few clicks to call up the two presets, and voila! The processing time required by a reasonably powerful, fairly recent pc running Sound Forge would be a few seconds at most.
If you want to pursue this approach, I'd suggest starting with the free audio editing program Audacity (easily findable on the web). I haven't used it, but conceivably it might be able to provide similar functionality.
Regards,
-- Al