I have a Shark Model SV75Z_N with the same switch and circuit board. After checking out which wires and circuits were affected by the switch with an ohm meter, I determined my problem was somewhere on the circuit board between the gray and black wire. The white motor wire was switched to the battery positive red wire on the circuit board and still worked fine.
I cut the gray wire close to the circuit board and spliced it to the heavier black wire from the battery pack to complete the battery negative to motor. It charges and runs.
I probably bypassed overload protection and who knows what else. Fire hazard maybe? At any rate, I'm not going to leave it plugged in when I go to bed!