I’m imagining a mosquito net set up like a tent.

That’s what I would do. Hook jumpers from the buzzer to the play button of an mp3 player. That way if the music system fails, the buzzer still wakes you up.

My cat could. But only because I would rub my fingers together to make a faint noise, so they could tell where my hand was without looking.

It significantly reduced the number of surprises, and they felt a lot more comfortable around me.