I spoke to Avalon Hill about this haunt because we were having the same issue. I'll put their response below.
Spoiler (click to reveal)
"In order to Open and Destroy the voicebox, you simply need to have picked it up. Opening and Destroying it is a free action that wasn't clarified in the text. Remember that before you can pick it up, you'll need to find the correct number of uncursed spell books." So the heroes just need to collect the right number of books and move to the room and pick up the voicebox. The traitor will tell them when they succeed.