Listening to internal mixer cue with external mixer headphones - djay pro for mac

My set-up has djay pro for Mac, a single turntable and a 2 channel external usb mixer. I’ve got the turntable linked to 1 channel and my mac linked to the other via USB.

I’m not using the external mixer capability in djay pro because I’ve only got 2 channels on my mixer, so my question is – how can I keep using the internal mixer on djay via a single channel on my external mixer (and I’m happy to use the cueing function in djay) but listen to that in my headphones which are linked to my external mixer ? I could keep switching the headphones from external mixer to mac built-in output depending on if I’m trying to mix in a vinyl track or 2 tracks in djay but that’s a pain.

Would an external soundcard help me with this ?