Electronic component that is like an LCD version of an LED?
The closest thing I can think of to what you're describing is an LCD light valve. It's a single piece of LCD glass with two electrodes on it. If you've ever used a self-darkening welding helmet, this is what's used to make the window in those. Most of these will probably be bigger than what you have in mind, though.

If you plan on manufacturing this product in quantity, contact an LCD maker. They make custom LCD glass designs all the time -- you could probably get a real "compass" design made, instead of just a single indicator.