The accounts of the seconds were at odds as to which man fired first. This is because the seconds had their backs to the duelists, in order to provide a certain level of deniability. Dueling was by this time illegal in both New York and New Jersey. If Hamilton threw away his shot by firing wide--as he'd proposed to do--he may have fired first. Logically, this would show Burr that he meant no harm, but, of course, it would also leave him at Burr's mercy. How Burr reacted would then be up to him.
If Burr shot first, as Pendleton later declared, his shot would have hit Hamilton and caused him to spin about, clutch at his weapon, and discharge it harmlessly into a tree. The passage of a .54 caliber ball is not easily overlooked. Whoever shot first, we know the outcome.
In the winter of 1800-01, during the disputed election between Jefferson and Burr, the Electors had deadlocked, throwing the election into the House of Representatives. Thirty House votes would be logged before this impasse was resolved. Hamilton worked tirelessly to block Burr from assuming the presidency by writing to his federalist friends in the House, saying that Burr “is bankrupt beyond redemption, except by the plunder of his country. His public principles have no other spring or aim than his own aggrandizement.”
That morning by the river at Weehawken, Alexander Hamilton threw his shot away and left himself at the mercy of his enemy. I'll have to quote Trelane, the super-being in the original Star Trek Squire of Gothos episode and end it here: "...your heroic Alexander Hamilton."