how to play engineer without ever shooting
you will need Dominate
Use overload to break down the shield of the enemies and then use either Dominate or AI hacking to control an enemy once the shield is down. Send your Combat Drone(with explosion) to stand right next to the controlled enemy to attack it and to draw the enemy's fire away from the controlled unit while it is under your control, when the drone explodes it will heavily damage and likely kill the controlled unit. Repeat this till their is only one unit left then just take him down anyway you want.