I suppose it was easier to have someone actually shooting the washer while the actors (in the frame) take their own "shot", besides which the sound and effect of the washer actually being hit by a bullet would be very different from shooting a blast of air at it. (Not to mention an air blast would make a noise, would probably be more likely to miss the washer than a bullet, and wouldn't "push" the washer in a realistic way.)
As for using a marksman, he would almost certainly have been able to hit the thing right off, or at worst in two tries: that's why he's called a marksman. Depending on how the camera was angled, the washer may not have been as far up as it looked in the film. Finally, it would make no difference whether the marksman actually shot the bullet through the center or not. All we see from the ground is the washer being hit. A different washer with the stamp already "shot out" would be all they needed to create the illusion of an expert shot.