Here in NH by law you have to use a 20 ga with at least #6 shot. I have taken birds with both my single shot 20 and a long barreled 12 ga. One pellet in the spinal cord in the neck will do it.Check best rated gun safes here: http://www.zentiz.com/best-gun-safe-reviews/
I have called in birds that could have been killed cleanly with just a .410, so yes the 28 would do the job within a reasonable distance.
Good luck !
I think your should do it. I have shot a lot of Turkeys with a 20 Ga Pump.a 28 ga at 45 yards is somewhat pissing in the wind at a turkey Good luck