Have you tried using roomBounds yet? This allows you to set lighting conditions and HDR reactivity to each individual area, at least for interior cells. I'm not sure if this works with exteriors (ie: areas which are set to use a skybox/sun-light)... I'd be interested to know though.
You may also be able to set an individual cell's light data to something non-sunny... but I doubt that would be a feasible workaround. Parts of the area outside the cave would have that dark lighting, unless the cell-border is INSIDE the cave's entrance and Player cannot otherwise enter the darkened cell(s) while still outside... like if the cave was at the bottom of a steep cliff/mountain.