This sounds like it only changes the framing, but in reality it would lead to completely different behavior, so the "leave the gun alone" option would likely lead to far fewer deaths than the red button option, simply by virtue of organisms including humans being generally biased in favor of "do nothing" (= leave the gun alone).

You could do both experiments with dogs instead of humans and roughly 100% of dogs wouldn't manage to shoot themselves with the gun, whereas if you forced them to press one of the two buttons (e.g. keeping them in a room until they press one by chance), roughly 50% would press the red one. So the two experiments differ strongly w/r/t to how likely it is for a "non-thinking" organism to choose each option.