To kill Alien Troopers without shooting, when the Alien Troopers jump in the air and levitate shortly doing nothing, they are about to charge at you and possibly kill you in one hit. When they do this, get out of the way. When they charge and miss, there will be an instant where they are idle. Run up to them, grab, and throw them. This may be slightly harder at certain angles. The moment you throw them, they will die (under the Easy difficulty setting at least).