You're never going to see other kind of Khajiit in the games - Too many subraces with too little payoff.
Hypothetically this is how it could be done:
Ohmes: Look almost like Bosmer save for their tattooed faces and smaller statue.
Ohmes-raht: Like above but with short fur.
Suthay: Smaller suthay-rahts.
Suthay-raht: In-game khajiits.
Cathay: Bulky suthay-rahts.
Cathay-raht: Super-bulky suthay-rahts.
Tojay: Nothing known.
Tojay-raht: Nothing known.
Alfiq: Intelligent housecat
Alfiq-raht: Unknown, probably larger intelligent housecat.
Dagi: Skinny and smaller suthay-rahts.
Dagi-raht: Skinny and smaller suthay-rahts, though somewhat larger.
Pahmar: A tiger, for all means and purposes.
Pahmar-raht: A larger tiger.
Senche: A rideable tiger.
Senche-raht: A larger rideable tiger (battlecat).
Mane: Exists in-game.
So what does it boil down to:
1.) Ohmes (could use Bosmer-skin for game-purposes)
2.) Ohmes-raht (could use reskinned Bosmer-Skin)
3.) Khajiits that (assumedly) look almost the same and can be represented as the same (Suthay, Suthay-raht, Cathay, Cathay-raht, Tojay, Tojay-raht, Dagi, Dagi-raht)
4.) Alfiq and Alfiq-raht (intelligent housecats without the ability to talk)
5.) Pahmar, Pahmar-raht, Senche and Senche-raht (all tigers)
6.) The Mane
Honestly though I don't know how the moon-cycle-based appearance could be worked into the game. The simplest way to do it would be to assign every Khajiit a trait according to a certain time span he was born in and stick with the same look for everyone. But then we also would need a mechanism for the Mane.