How to clean a Chanel Bag?

I won an auction for a white Chanel lambskin quilted bag. Looks like I
will have to clean a small bit of dirt from the back of the bag (and
any future abuse!). I can't find any info about the best way to clean
one. I have the leather cleaner and conditioner from Coach that works
great on their bags, but I am not sure about the Chanel leather, which
is softer and maybe more delicate.
TIA!
Beth