You'll get much better advice on this over in the oneworld forum. However, I don't think you'll be able to use the ORD-DEL flight since there is no non-stop service from SA-ORD and I don't believe you're allowed to hop around NA using the SA-Asia exemption. Others in the oneworld forum will know better if this is allowed.

Your best and most comfortable bet is probably EZE-JFK-HKG-DEL on AA/CX although EZE-(SCL-LIM)-LAX-HKG-DEL (3 OWE segments only, about the same mileage) is also a possibility there isn't availability through JFK. You could also route JFK/LAX-NRT-HKG-DEL if you want to upgrade on AA.

Michael