Yes, I agree. There would need to be another wire attached to the stylus in order for the squibs to activate. Also, given how elaborate the set-up was, I don't understand how he was able to simply reel the wires back in without disturbing anything. Also, he forgot to shut the window at some point in order to prevent the door in the back of the room from closing whenever someone opened the door from the main hallway.
Yeah, Michael, a unique part of that Bye Bye plot with the other Mensa members was that each one of them offered-up a truthful tidbit to the case that, while framed as insanely goofy or dumb ideas, was actually correct. Even the dude who invokes "up the chimney" wasn't off base either.