I wish there was a Lower Decks and VOY/DS9 version of this. However, I would cry a little having to design any PCB for that space, even if it's as simple as registering a button or blinking an LED with a microcontroller.

Honestly, I'd be tempted to just do analog FM instead of Bluetooth and basically just make walkie-talkies. You could enable greater functionality, perhaps including Bluetooth support and being able to make voice commands, by having a "ship's computer" that would just be a Raspberry Pi server or something with an FM receiver that could process the voice commands and route signals. You might have to hide it in a probe like a tricorder or a phaser while at cons, but if you're just handing out Halloween candy or something like that, you shouldn't have to worry.