The SQWAK, if you forget ATC will remind you during push back. Had it a few times.
The Horn with APU off you will definitely hear it. I did a push back once on battery only and it was so quiet (no avionic fans running) that we could actually hear the ground mechanic talking to the tow truck driver. And the main reason for the horn, is not for saving the batteries but to avoid the ADIRS to overheat. As if you are on battery only, there is no avionics ventilation at all.