音楽ガイドラインでは
カラオケも口ずさみもダメって書いてあるな

https://www.twitch.tv/p/legal/community-guidelines/music/
Karaoke Performance ? Singing or performing to a karaoke recording other than an in-game karaoke performance that is licensed for you to share on Twitch, such as a Twitch Sings Performance.
Lip Synch Performance ? Pantomiming, singing, or pretending to sing to music that is not owned by you or is not licensed for you to share on Twitch.