I book AA code shares all the time. Call AA and ask them for the CX PNR from the booking. It is different from your AA one. Once you have it, you can login to the CX website and select your seat using the PNR and your name. You may have to play around with your first name and middle name in order to get in. Try just first name, first name middle initial with no space and the first name middle name no space. One of them will let you in.

Once in your OWE status will let you select an appropriate seat.