The Hand Cannon becomes available once you reach Finkton Proper/Worker Induction Center (you'll know as Finkton will call you while in an elevator). You are then given several items by an attendant, this includes some Silver Eagles, Salts, and a Hand Cannon.
The HC is fairly powerful, able to kill enemies from medium range. The best combo I've found is Shock Jockey and then a headshot. Even in 1999 Mode, this combo usually on takes two to kill common enemies.