If you are fully coupled the only way to get off the ILS is to either (a) press GA and immediately Alt Hold or (b) disconnect the AP and recycle both FDs which is a bit of a faff...
The easiest way as mentioned is to fly the approach in LOC/VS then just reduce VS to zero at the circling altitude and turn towards the downwind. *using one of the above techniques when you screw it up and accidentally arm approach anyway