From my own attempts to analyze the Planet Killer, I'd say its core is made of wood; what you can see of the interior of the maw (the part without the special effects) looks like roughly carved/dug-out wood to me. And we know that the Enterprise
miniature itself was mostly made of wood, so it's consistent with the techniques used in the day.
But the exterior is definitely wrapped in sheets of some clear plastic, though it looks thicker than cellophane to me. It's really remarkably crude when you examine it closely, considering how effective it was.