Cannot mute myself while sharing a video during a recorded meeting

This is follow-up to another thread that didn't seem to be resolved.

I need to share a video that has audio, during my recorded meeting. To do so, I share the video and select the "Share Sound" checkbox, and because the video has audio and I'm in a noisy environment, I mute myself.

However, I noticed that if I do that, the Recording Alert window pops up, warning me that unless I unmute myself, no audio will be recorded.