I looked it up trying to be helpful. Supposedly, bone conductive can overstimulate the nerve clusters - resulting in an attack of sorts. Most likely because they press on and vibrate the temples.

That really blows. I'd rather lose a finger. Sorry to learn of it.

In the spirit of the request, I would suggest beanie headphones. Assuming it's cool enough out, and you can tolerate a beanie, they may fit the bill.