Place the skybox camera at the ORIGIN on the whole map space. Select some primary blocks (such as major floor brushes, etc). Select the skybox camera Copy it all, drag it below your map. Scale it by 1/16 (times 0.0625?). Remove original skybox camera (not the copied one). Make skybox geometry around the shrunken primary blocks. remove or NoDraw those copied blocks (as they are in the level already, right?).
The skybox camera projects the world onto the skybox texture from the origin of the map. Therefore it needs to know the relative position of the world objects from the origin, and matches that from the camera to the skybox geometry.
So the "Main brushes" would be the water brush(es).
Place the skycam at the origin. select it, and the water, copy and move below the level. Use the "translate" function to scale by 0.0625. build the 3d skybox area (ie the water around the now very small water brush) delete the water brush you copied down, replace with a nodraw brush (to seal the 3d skybox room) done? also scale the texture 0.0625*0.25 (default)