LightDims sells fully opaque stickers to put over bright LEDs. (In addition to stickers that simply dim them, of course.) I put one of these over my camera, with the end folded over to make a tab. It's a full hardware solution, and I can remove it and replace it as needed when I (rarely) use the camera.
Oh yeah, and since it's glossy black, it matches the existing surface, so it's not very noticeable.