I camouflage our conversation with loud music to avoid recording.
That's the sample sentence I'm suggesting. A work that you can use, quite rightly, is "camouflage". In this context, that word works great.
Here's another example of a sight-related word used in other contexts. Just as the word "beautiful" may first and foremost tend to refer to sight, but can also apply quite nicely to music, English has no problems taking a concept that is often used in one text, and using that concept in a totally different way. (I would say that doing such a thing is typically less atrociously egregious in concept than when a person "verbs" a noun like what this sentence just did.)
The most traditional use of the word "beautiful" may refer to sight, but the word can often mean "nice" or "pleasant" when referring to sound, or even something unrelated to senses, like the "beautiful work" of a job that was well done. Similarly, the word camouflage isn't at all restricted to only refer to sight. For instance, lies can often be effectively camouflaged by a bunch of true facts.
If you try to make your conversation appear to be part of background sound, by making the background sound at least as loud as your conversation, then your conversation will effectively be camouflaged by the the loud music.
People hearing or reading such a sentence will totally be able to understand the concept, without difficulty.