Why not just bring the puppy to a shelter if you can't handle it? I don't think there's anything wrong with saying, "you know what? i'm the wrong owner for this dog, so I'm going to surrender him/her and hopefully find a dog who is a better fit for me."
I think rarely a "behavioral euthanasia" might be necessary, but get it done at the vet's office. No dog deserves their last experience on earth to be of their beloved human shooting them. This isn't the 1800s.
One of my brothers shot his dog as a means of euthanasia - dog was old/dying, and he told me he bitterly regrets it. I told him that my end of life plan for all 4 of my dogs should they not pass away in their sleep is that they will pass away in my arms with me petting them telling them how good they are, how much I love them, and that they'll feel better soon and we'll go to the puppy park and romp and romp and play and play. I just don't want them to be afraid at the end. They deserve better than that.