Best way to stream video and audio to 2 different devices

Question

I have a computer (Mac) from which I stream video and audio to a ChromeCast which is connected to a projector (HDMI and RCA audio/video available as inputs).

So, currently, both video and audio come from the projector.

However, I would rather use a remote speaker (bluetooth one but wired input is also available) to output the audio.

The only solution I have found is to mute the audio on the projector and open another app (on my computer) where the sound will come from my remote speaker.

However, I am looking for a more "clever" solution such as: - splitting the video and audio after the chromecast (thus using RCA to plug the audio to the remote speaker) - only cast the video while sending audio to the remote speaker with Bluetooth