The text in the link says it's a "tiny 1.5-inch barrel." If so, the accuracy would be quite limited. The relic firearm shown might be useful at a very close distance, like in a phone booth, but not much beyond that. Also, any persons close to the shooter would have heard the shot.

And finally, the physics: Charlie's body was thrown to his right, indicating a shot that came from his left... not directly in front of him.