How to use a HDR Skybox for U5 ambient lighting, but *not* background image?

I have a good forest HDR skybox I'd like to use for lighting to make use of the environment lighting in Unity 5. The problem is, I don't want the forest image appearing as the background.

In camera settings I see that I can switch off the skybox and use a solid color instead, but there's no option for a regular background image. So the problem is, how to I use the HDR forest for lighting, but have a regular cloudy sky skybox as the background image?