According to the just-released Khan #5 comic, it's due to facial reconstruction, memory wiping, and vocal cord manipulation. Thoughts?
That sounds ridiculous. He was recast, nothing more, nothing less. Look at Saavik, Cochrane, Scotty, Ziyal...
Plus, Khan Prime's skin colour changes between "Space Seed" and WoK anyway. He goes from awful faux-Indian brownface to Montelban's natural white skin tone.