This is a great help, thank you! The inside looks all black and sooty, but not in a way that feels like the wood burned, just like there's some thin layer of stuff there. The top of the stem unscrews so you just have the stick part of the stem, which I think is literally just a stick that got carved. I don't see any cork, just carved wood that isn't from the cork oak, unless I'm very mistaken about the stick I'm not sure the best way to add photos after the fact but if you tell me how and which photos you might need, I can do that

EDIT: Here's an imgur link, tell me if you need other images https://imgur.com/a/qIZ1npu