DaSilva (player) can pick up alien weaponry, but CAN NOT FIRE THEM! If you do fire one accidentally, you can Reload the Last Checkpoint and save your achievement.
Your squad agents can use alien weaponry without affecting this achievement.
Alien weaponry consists of anything with Laser or Plasma in the name, as well as Sticky Grenades.
Lightning weapons and the Microwave Gun are human technology and thus are safe to use while trying for this achievement.