I had a friend of mine do that to his beagle but one pellet for some reason went farthur than the rest and he lost a good dog, it just took one pellet.
Tom, Kathy, Nikki, & Kelly
Pets: Lady - Texas Heeler, Dinger - Rhodesian Riidgeback Mix
2008 Ford Expedition Eddie Bauer 4x4 5.4 ci 3.73 gears
2008 Dodge Ram SLT Big Horn 4x4 5.7L Hemi 3.92 gears
2007 Jayco Jayfeather EXP 254
Husky W/D, P-3
Just about the worst thing to do when a dog is running away is to chase them. If you can get their attention, or get them to look at you, run away from them. Most will chase you as part of "the game".
As to another point, I, personally, would not shoot a dog, or any other animal that I did not mean to kill, with even the lightest of loads, or a pellet gun or BBs.
After years of runaway dogs, I finally trained mine to come to me when I use one of those clickers. The clicker noise interrupts their concentration and I trained them to think that the clicker meant I have something good for them. First it was treats, now it is just pats and kudos. Click and walk in the opposite direction - mine follow me now.
As others have said - NEVER play "chase". Ever. ALWAYS reward a "come" - even if you want to kill the dog (and they can detect that, too....LOL!) and practice, practice, practice.
Plus a *thought* - train your dogs to come to a whistle, too. If they're a long ways out - they can hear a whistle better than your voice. Also - a whistle doesn't transmit that "I'm going to kill you" tone of voice - it's just a nice neutral sound :-)