Because just about any weapon would do, the Stun Gun or Tranquilizer Rifle are prime candidates for the purpose of this achievement as both can be acquired right off the bat in Dubai if the non-lethal option is picked. For both, the player will only need to focus on ammo capacity upgrades, which wouldn't take all that many crafting parts to do, and getting a laser sight which is sold by several vendors in the area.
Another option for the task would be the Devastator shotgun, as it will only accept three damage upgrades and nothing else. It can be bought from Mikael Mendel's shop after returning to Prague from Golem City. A free Devastator can also be found in the security chief's office in London.