The thing is that if all you want is to use a custom texture for your sky, then you should just use the MAPINFO texture option rather than using a skybox. You should only use a skybox if you have textures that are specially made for a skybox (and thus account for the distortion). Programs like Terragen can do that. (Quoting from
Unreal Wiki: "Due to the way Terragen renders and the parallax effect of the skybox only a simple cube is needed for the skybox brush. Spheres and cylinders are not necessary.")
For example, importing E1M1 in Doom 2, I made a noob mistake by trying to use the proper sky without overwriting Doom 2's skies, and simply used a cube skybox with Doom 1's sky (imported as sky_de1m1) along its walls. It was awful, as you can guess. Attempting to round up the skybox solved nothing, and just made aligning the texture harder. And there was no satisfying solution for the top side... Then I just removed the skybox entirely and used MAPINFO, and miracle, it was nice.
The moral of the story being that if you don't have a sky that is meant to be used for a cube skybox, don't use it for a skybox.