Instead of a skyBOX, try a skyDOME (not sphere) - think of an upside down saucepan. Then adjust the fog distance settings as necessary. Ensure 'fog on' is applied to the dome. You will probably need to model the dome in a suitable application but is simple to do (ie flatten a sphere).
The skydome shape ensures the "sky" above the player is quite close, and less (or not at all) affected by the fog, whereas the fog density builds up gently and uniformly in all directions when the dome begins to slope down to meet the horizon.
This doesn't work with a skybox, as the linear distance to the corners of the box is greater than to the sides, creating a less pleasing effect.
The simplest misteaks are the hardest to spot.
