This uses 2 images, 1 panoramic image for the model, 1 small 256x256 texture for radiant.
In asset manager there is a sky non-cubemap option. You'll need to make a skybox xmodel (basic polygon sphere in maya works fine) or use "test_sphere_silver" and change the material.
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Gdt settings for model material
Skynoncubemap sky sky, Depthtest less, Depth write off, no tile, nomipbilinear, nopicmip, no impact, no marks, no light map, no dynamic light, no fog, sky.
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The non cubemap skys don't work for a radiant texture so you will need to make one.
I used an all black 256x256 tga with these gdt settings (it's purpose is for launcher /compiler)
World unlit, Blendfunc Multiply, depthtest less, Depthwrite off, No impact, No marks,No lightmap,No dynamic light,Nodraw,Nofog,Sky
Blendfunc option could be add or multiply depending on the color of your skybox.
Apply the radiant texture to the inside of a caulk box surrounding your map.
Test in a new map incase you make a mistake.
Add model to _patch and worldspawn
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Your xmodel skybox will project itself to the caulk box in radiant.