Single party consent for recording in public (or in places a person could be reasonably expected to be recorded) is the norm everywhere I’m aware of.
A private conversation would be one where you could claim that a person is expected to read a privacy policy to people but of course that would be preempted by the recording party following actual laws governing recording and would never be expected.
You’re barking up the wrong tree and fucking up your life by doing this.
Split the streaming/gaming duty to a different device that can be operated in the way the user expects.
Wherever you disconnect shutdown signals from will be relied upon by something down the road and you’ll end up with a weird messed up broken update when that happens.