The custom used to be (maybe still is) that you call the sheriff and he handles the problem with a gunshot or calls some other authority. Makes sense.
But the shut up part only works if you didn't blow doggies brains out in front of a bunch of kids!
Had to put down my dog recently, dying of a brain tumor. Dug a hole out at my brother's country place. Topical application of a lead ‘pill’ to the back of the head. I miss that dog so much! But I didn't do it in front of any children! It was traumatic enough for all involved already!