Even if you’re somewhere without good cell service or wifi (so, most shows!), there are bluetooth walkie-talkie apps that would be perfect for this. Nearly all phones have bluetooth now, and you’d just have to be within range.
I’d think the other problem with a shower curtain, even if you duct tape is in place, is that it’s going to be a bit noisy if there’s wind, too. Which would be problematic for both scribes/judges and horses!