Transfer desk is not a thing in the US... we don't have exit immigration control so there is no sterile zone on departure.

Since your post 2 days old, I assume your wife got on the the CX flight without problem. But if someone is searching this thread later for the same information, there are several ways you can obtain boarding pass at TBIT air side:

The first way is the most obvious... you can check in online via your phone.
The second way is to use the automated kiosk. There are several located throughout TBIT air side and at least 1 in the T4-TBIT connector.
The third way is to show up at the gate and get paper boarding pass.