Can a webinar participant share their screen while muted?

We want to host a webinar where the audio from the host's computer will be the only audio used by Zoom.   Other participants audio input to Zoom will be muted on their computer.  All participants are in the same room and are using external mics which are connected to a mixer.  The mixer output will feed the host's computer and be the source of the audio for the webinar.  We want to do this to better control the quality of the audio.  Since other participants Zoom mic input is muted, Zoom cannot use their audio to recognize them as the active computer.  We still need the participants to be able to share their desktops full screen.  How do we accomplish this?   One idea I have is to have the host spotlight them when they need to share their desktop.  Will this work?   Is there another method which will work?

Thanks.

Jim Norman