If you don't want to go into difficult carving (which would be a nightmare on a piece like your Davy Jones' beard) You can use a soldering iron or any pyrography tool to draw patterns on it.
Actually any hot enough metallic item could leave interesting graphical effect on wood.
The black curved mark on the bottom left part of the photo above has been burnt like that.
With a clear wood like your Cthulhu's you could obtain damn good contrasted effects, I bet.
Be careful with possible toxic stuff while heating the glaze though (or even the wood itself), better wear some protection.