Using nvidia hw, I get no visible distortion (that I've noticed) with cubemaps on any q1 map I've tried (including id's maps). The intel hw in my eeepc is another matter, but it doesn't get the walls right, let alone the sky :/.
Blender exports cubemaps with all 6 faces in the one png. I'm not certain about the details of setting it all up, but if you model a full scene in blender, you can make your own cubemaps

. Blenders cubemaps are 3Nx2N (N is the resolution of each face) with (bk rt ft) along the top and (dn up lt) along the bottom (normal quake suffixes). QF's glsl_bsp.c has code to load such files.
For the skyboxes you posted, they're already nicely setup (separate negx/posz etc files), but if your shader is setup for ft/bk/... skyboxes, you'll need to swap things around a little.
I reckon you want that second skybox for the girl

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