can I route the audio of voiceover to a different output device while on a call?

Hi all, when I'm on a call and I have a bluetooth device like a speaker connected, is there any way for me to have voiceover audio routed to the speaker while the rest of the audio goes through my phone, or vice versa? Although I have the audio destination option selected as a rotor item, it doesn't show up. I can only seem to choose where voiceover audio goes if I'm playing music through an external device.
I realize this may be an odd request, but here's a brief explanation of why I'm trying to send voiceover audio elsewhere while on a call.
I've been asked to do a demo of voiceover on iOS, and we're using a piece of conferencing software that allows me to share my phone's screen. Unfortunately, there's not an option to share audio, so I thought of logging in with a second device, muting my phone microphone, and placing it near my laptop microphone as a workaround. Unfortunately, even with only 1 microphone active, this approach results in feedback. When my laptop picks up the voiceover audio from my phone, it is sent to the meeting room, and my phone's speaker also plays whatever audio is in the meeting about a tenth of a second later. This, in turn, is sent to my laptop, which creates a loud squealing feedback sound. There is not an option to mute my phone's audio from the meeting. As such, the only workaround I can think of is to have voiceover audio routed to a speaker, place the speaker near the laptop, and have the meeting audio go through the earpiece of the phone. Since the phone won't need to be near the laptop microphone, the feedback issue will not occur.
Please let me know if you have any workarounds or suggestions. Thanks in advance!