I have used the <$2 tiny ball compass sold by Walmart multiple times at depths of 100'. Normally it's on my gear bag as a zipper pull, but I've loaned it several times to guys that had rental gear with no compass in the console.
It's not precise since it's less than 1" in diameter, but it's easier than a normal compass to use for general orientation.
If you do decide to try one of the more traditional "Boy Scout" type flat compasses, be sure to get a liquid filled one ---- it will probably survive the pressure. Based on my experiences on boats though, the springs that hold the compass to the bezel plate will probably rust, making it hard to rotate the compass bezel.
Good luck,
Charlie