Presumably you don't want to touch the desk at any point... so...
Easiest way is probably with an A/B XLR box - and route your mic to 2 channels, one with reverb, one without. It's quite useful as you can set the volume differently and EQ the voice differently for singing vs speaking too. Of course, you would need two wire runs for each vocalist if you wanted to all speak between numbers - and this may eat up your channels pretty quick.
Or... you could set up an alternative scene that is identical to your "playing" scene but without the reverb. You could switch between scenes via MIDI. The MIDI implementation on X32 doesn't seem that clever at the moment. It may improve with firmware updates. I'm sure you could get some pretty small like the MIDI mouse to do it.
In short, not going to be cheapest for just switching reverb on or off. - I don't think these things are not necessarily designed to be unmanned.
Umm, that's me out of ideas.