'Asian-flavoured' classes generally serve one of two purposes (or both):
1.) To impart an Asian style of magic that is unattainable or difficult to 'flavour-in' to Vancian casting.
2.) To impart Asian styled Kung-Fu.
Conan doesn't need either of these, and really can't support them to begin with. Plus, Khitai is more of an India/China hybrid (caveat: as I see it), and most Asian-flavour sourcebooks in the d20 system are predominantly concerned with Japanese style additions, which would seem out of place.
So, there's really nothing you could need for Khitai that isn't covered by the base classes in the main rulebook, as well as the ever-useful multi-class combos in the various splats. Flavour is flavour. The crunch stays the same. If you want to impart more Eastern flavour to your Conan game, you can do so with vivid descriptions and so on. The crunch is just fine as-is. And you'd probably be hard-pressed to find something for Khitai that isn't adequately covered under the existing Conan rules.
Even renaming the classes isn't really necessary. In my games, most 'Soldiers' don't actually call themselves Soldiers, unless they're part of an actual army. Pirates can call themselves Freebooters or Privateers, or just scoundrels, adventurers, raiders, etc, ad nauseum. So, grab a Soldier/Noble and call it a Kisatriya. Bingo, bango.