In theory this could work ... A sneeze does have a lot of power people easily underestimate and there are ways to kill by shooting without gunpowder, however, the power might still not by far be enough, but still, ya never know... but even though I sneeze a lot, I cannot control my sneezes... I might as well need a can of pepper with me... So in the end I guess this will not replace a gun.
Of course, this is "troll science" so it was meant from the start to come up with something that works in theory, but which would very clearly never work for real.