Hide Lens Flare From Certain Cameras

I have a scene in low Earth orbit where I have a skybox camera that renders the skybox material, a small planet model that rotates and a directional light for the Sun with a lens flare. That light only affects the planet ('Skybox' layer) and doesn't light any of the other layers but both the skybox camera and the main camera see lens flares on it w$$anonymous$$ch results in the appearance of two Suns.

Is there a way to exclude some lens flares from a camera without disabling its flare layer so it can still see other lens flares?