I think the “key” (the headband) only lets you through the stone doors from the enclave library to the underground passage. I don’t think it stops the statues firing, though it feels like it should. That said, I think I only tried it with Findal’s headband, not Nettie’s.

"You may call it 'nonsense' if you like, but I've heard nonsense, compared with which that would be as sensible as a dictionary!"