That's a lot of challenges in one shot, you might get out on the web for tips for capturing birds in flight, that's the closest scenario that I can think of.
If it we're me I'd start in Tv because you are going to want to control movement of the exploding pigeons, I looked for pictures online (there aren't many) and IMO too high shutter speed will give you a boring picture of chunks hanging in the air; you really want to capture the blur of movement.
You'll be metering against the sky, you might try metering a pigeon beforehand and manually set exposure. Sunlight from behind will help but you can only control that slightly.
The short lens will be easier to capture the explosion in-frame, but if you go that route use your lowest ISO so you can crop without losing as much quality. I'd use a 50 1.8 over the small zoom because of image quality.
While you are there...pics of the gun discharging and of shell ejecting can make nice pics as well.
Just some ramblings, best of luck with your shoot!