VOX should work fine, you need a close pickup mic that attenuates well (not sure what to recommend) and some way to change the VOX threshold on the radio. Helicopter pilots do the same thing, you can hear them incredibly well considering the amount of noise they're shouting through. A push to talk button would be a big distraction to a racer if you ask me, they're already busy enough trying to drive, adding another button is going to hurt performance. CB radios have a squelch control which does the same thing, when it's turned up high the incoming radio signal has to be very strong in order for the receiver to output audio. You should look for radios that support those features. Do some more search on Google, you should easily be able to find a commercial product that's not too expensive that meets your needs. So the three key features you're looking for are a mic with high attenuation, a control for the VOX threshold, and possibly a squelch control.