Having filled up the third pill bottle in about six years, I decided a better solution was needed:
Often referred to as a "sharps container", variations is available for cheap at your local pharmacy or medical supply store. While the tub is ugly, it's also sturdy, near unable to open once it's sealed, big enough for years and years of shaving and can be handed in for safe disposal later.
Overkill? Perhaps - but better safe than sorry, and unlike an old pill bottle or a slot in the wall it wont cause a nasty surprise for someone else down the line.