I would have thought a cz was a little over kill, way too powerful for sheds, wouldent want holes in his roof would he
how about either a 9mm garden gun, or probably better a decent air rifle,
head shots will bring them straight down, body shots they can fly around spraying blood
Im presuming ferels are in there too
for the proffessional look, have a partner, he's your torch man, lighting up the pigeon to be shot, then after switching off, until the next one, saves spooking the birds, he can also bag up each bird as its shot, before the next, saves missing picking up a dead one,