Ouch.. that gets tricky. If you happen to be in that situation..
call delta and see if they can do it..

if not, call NW and explain the situation.. (let them put a note on your account)
then call delta again.. tell them to delete those miles from your account and
post a confirmation on your account, or mail you a letter..
now send that letter and the boarding pass stub to NW for the credit.

Provided you do it within the allowed time frame, and confirm this with
NW prior to taking any other action, you might be able to do it.

I always had this issue with DL in the past. They would not let me put CO#
automatically.. and somehow my DL number will appear on my
reservations when i check in.. but the above two things worked well for me..
I've generally done this within a week or two of my flights.