Sorry for the late response. Thank you ladies for your kind advice!
I took it to Chanel and they wouldn't take it because it is python(I always thought it was water snake skin for some reason!).
Chanel recommended this leather specialist located right on next block from their Rodeo drive store. The place is called "Stephani's" Apparently, there was no way to clean the delicate leather but the owner said he can re-dye the whole bag and make it perfectly even out. It only costed me $200 and it was the best thing I've ever done to it.
Python bag's color was fading a little bit and lambskin on chain strap had some darkening before. But now my bag turned out like a brand new exotic skin bag, only much brighter, stunning coral-red color!!! I was so happy with a result and I want to recommend this place to anyone who needs great repair job done for their precious handbags. He treats all kinds of leather, fix handbags and shoes to perfection!