If I were to download this, I'd do it with some masking tape over my webcam, booted from Kali Linux, inside a Windows VM from a library or coffee shop.
what people always seem to forget is that it's not the webcam but the microphone that presents the greatest privacy risk.
if you tape it off, it'll just lower the volume (and possibly dampen higher frequencies, but you just need 300-3800Hz for voice).
additionally (outside the coffee shop scenario you describe here), what's a webcam do? ok, it'll see your face. chances are they already know your identity. maybe it'll catch one second of your underwear, big deal. now compare to a microphone, much less data, but it picks up every conversation in the room, regardless if they're "in view". much worse.
Different people have different rankings of what they consider to be a privacy risk. From recent news, we know that some people are very much into distributing personal images made by other people and kept in what was presumed to be private storage. We also know that some people enjoy manipulating images, including sometimes to torment those who have been photographed. Audio manipulation is less disturbing.
Consider also that some people have computers in line of sight of where they have sex, and an illicitly captured video recording of sex without sound is more often thought of as a privacy intrusion than an audio recording without video of the same ... as the noise from my neighbors might attest.
Would you do that on a laptop hard drive partition or on a clean drive? Would you use that drive after formatting it? I think that physically breaking the connection between the camera and microphone and the laptop would be a good idea.