I have no idea whether anesthesia is used for lethal injection in human beings.
I can tell you than in animal euthanasia, the animal is put under general anesthesia prior to intracardiac injection. If someone was sticking a giant needle directly into your heart, you wouldn't want to be conscious for it, either.
Mader et. al. states that RAPID freezing (being dipped in liquid nitrogen) is considered an acceptable method of euthanasia for small reptiles (<40 grams). Larger animals may feel pain with this method, so it is not suggested for larger reptiles.
The one author states that freezing in a conventional freezer is an unacceptable method due to the potential for painful formation of ice crystals in the muscle tissue.
I agree that freezing a larger animal would be inhumane due to the fact that the body would take so long to freeze, the animal would most likely experience a long and uncomfortable death. For a smaller animal, I really wonder if the nerves are still capable of firing by the time ice crystals are forming.
I do agree strongly that it is better to cull deformed babies rather than attempting to nurse them through life. Even if they are capable of living a perfectly normal life (such as one-eyed or no-eyed snakes), selling it as a "pet" may be a great way to perpetuate the trait if the animal later falls into the hands of unscrupulous breeders. The only way to ensure that the trait isn't passed on is to keep it or cull it. Even the best-intentioned pet owner may have a change of life plans, especially with an animal that lives 20+ years, and you never know who might end up with it.