I assume you mean Chromebox? You can use external audio devices but they connect via USB, so in general this is one input - so you need a few things. A mixer with USB I don't think would work (not tried it) but the Chromebox expects a mono input and the mixers supply stereo. If you can borrow one to try it could be good news, and you will just need a microphones for your local contributors, and practically any radio mic plugged into it. If the mixer doesn't work then you are left with those horrible usb devices with an xor for a mic on one end, and a USB on the other. You would need somebody to work the mixer, to turn off the wireless mic while it's being passed around to the next contributor. You're going to have to experiment I'm afraid. Im also not quite certain if the voice cancellation will work on multiple mics with timing differences. The cancellation could be very poor and the system feedback?
You really are going to have to scrape around and borrow some stuff and try it.
Pretty well the main players in professional, licensable systems are Sennheiser and Shure, with plenty of other good brands around. For a handheld, the differences are small for speech so there are plenty of good ones to choose - but until you find out for certain it works, borrow or hire in.