Have you tried overwriting the 250x250px with the higher quality one? keep the same name, it should work. For example if you do a 2k skin or a 4k skin, it's in the same folder, same name. not sure you need to change the shader. AC will load any texture size, but keep it reasonable.
i watched that tuto a while when i started doing some skins, it explains quite everything, especially how to do extract specific texture from different parts using CM showroom. quite useful information...