You could do it this way (untested):
- Open Blender.
- Delete everything from scene.
- Add camera to center.
- Apply spherical skybox to sky.
- Set camera to orthographic, square resolution, about 4000x4000.
- Rotate camera to any 90° - 90° - 90° configuration (so it's always facing at right angles relative to the other camera positions).
- Render one image per direction (six total).
Now you should have six square images that can be used in a skybox. I think by using orthographic mode, you won't have problems with edges lining up, but it is untested.