I personally think it would have been a Conical bullet - only because of the distance the Confederates were shooting from. When you think about it, what are the odds of picking off General John Sedgwick from that distance with a head shot? He probably rode (or walked) right into the bullet's path.
The Whitworth rifle saw extensive use with the Confederate sharpshooters in the American Civil War, claiming the lives of several Union generals, including Major General John Sedgwick, one of the highest-ranking Union officers killed during the Civil War, shot on 9 May 1864, at Spotsylvania.