Please number (the) contracts and assign as appropriate.

'We kindly ask' is not normal English, and not logical. It is not kind of you to ask someone to do something. It would be kind of the other person to do something for you, and you would be grateful, so you could say

Would you be so kind as to number and classify the contracts?
or
We would appreciate it if you would number and sort the contracts.

You could also just say 'Please number and sort ...,' though that makes it sound more like a polite command, not a request -- as if they should have done it the first time, but didn't.

I'm not sure what 'zuordnen' refers to here, or why the people sending the contracts to the partners can't just number and sort them themselves, if they want them numbered and sorted.