Can a person legally mount a fake gun on an amateur-built aircraft?
Empirically, yes it's legal. I've seen several reproduction WW1 aircraft myself at airshows with fake guns, missiles or bombs attached. And I was once at an EAA chapter meeting where a member demonstrated his fake gun 'firing' using compressed air. There are also factory-built aircraft with fake weapons added later, by the way.
As to regulations on this, I've never seen one. Typically US laws and regulations state what you can't do, not what you can do. For example, there is a law that prohibits attaching dangerous weapons to drones.