Yes, when you completely rephrase the problem you will have different sentiments.
The thought experiment demands that the phrasing that was used actually be used, and you don’t get a chance to show the dumb blue people how smart you are before they pick their button.
The problem isn't rephrased. Option Red = 0% chance of death, Option Blue = chance of death but maybe you can be the hero and save everyone.
So we all choose option Red and you, the hero, chose Blue. Congratulations, we will write some nice words on your tombstone.