(Just in case someone reading this doesn’t know, I am a retired dog/cat veterinarian, so I am very biased.)
Reptile euthanasia is pretty heavily debated in the veterinary field, in large part because exotics vet med is a newer field, and there’s much less legit research data available to consult. Before I get into my personal opinion, here’s the definitive reference (for 2020):
The AVMA guidelines for animal euthanasia- reptiles on page 92
Officially, the recommendations there are those that have been agreed upon by the highest level of professionals- by veterinarians, and intended for veterinarians to use. When discussion of animal euthanasia comes up, the AVMA should always be consulted.
The laws surrounding animal euthanasia vary a lot, so I am stating here that I am not advocating/recommending any given procedure or product, and am merely sharing my thoughts. Officially, I only endorse licensed veterinarians or veterinary staff performing euthanasia in accordance with all applicable law.
In my experience, amphibian and reptile euthanasia are very very different. Amphibians absorb things administered topically, so there are additional tools available. For example, I used Oragel to sedate the axolotls in my undergrad thesis, then brought them out of anesthesia by placing them in a new bowl, with water with no drug in it.
Reptiles pose many metabolic issues, when it comes to traditional euthanasia methods in the veterinary setting. There are many horror stories of pentobarbital being given by a well-menaing dog/cat vet, the ‘body’ being returned to the grieving owner, and the animal wakes up half-way through their drive home.
My personal opinion is that no reptile should ever be placed in a freezer until it is 100% no-doubt dead (using the primary and then secondary/confirmation method). If placed in a freezing environment, reptiles maintain consciousness past the point of crystals forming in their blood. It is hypothesized that the pain must be unimaginable.
I have seen many methods of reptile euthanasia in practice. My ‘favorite’ is when an animal can be sedated heavily (to the point of anesthesia), letting the owner say goodbye, prior to pentobarbital administration. An alternative is to gas an animal down with iso or sevo, then use an ultrasound to visualize the heart for guidance as you do a heart stick with pentobarbital. ( @chesterhf - Using isofulourane alone will not kill a reptile, just anesthetize it. ) For all ‘ideal methods,’ it’s 2 step- first sedate heavily to the point of unconsciousness, then give the lethal drug. (Again, ‘ideally,’ there would also be the secondary/confirmation method, but this isn’t always used.)
However, culling neonates is a whole different thing, in a way. When it comes to euthanizing neonates that are clearly suffering (so a ride to the vet is out of the question), one thing you must never do (just as with any reptile) you must never use decapitation as the sole method- reptiles will remain conscious for quite some time afterward if they aren’t pithed. Decapitation is only ok as the secondary/confirmatory method.
In the emergency scenario, there are a bunch of things a non-vet could do. But, yeah, smashing the entire head, in one massive blow (as in obliterating between bricks) would be acceptable. I would think a pellet gun would be too small and imprecise to work- the brain may not be where you think it is (many well-intentioned, ignorant people try to euthanize their livestock by shooting them ‘right between the eyes,’ but that’s not where their brain is, so you get pretty horrific scenarios that result). If you do use a weapon, you should look while you do it, to make sure your aim is good- think of it as a gift to the animal you are euthanizing.
But here’s another scenario- let’s say you have a neonate that clearly has something wrong with it, is unquestionably not breeding material, but it’s not clear how viable it is as a pet. In these situations, if possible, that is where I recommend a herp vet. Sometimes they can tell conditions just with a glance- they can give you better info about the potential for it to grow into a healthy pet. Every now and then, they might come up with a fix for a problem. And, if necessary, they can euthanize in a way that is most likely more humane than most breeders are able to administer, because they don’t have the tools (controlled drugs).