I only found this one excerpt in the above link associated with reptiles:
"Rapid freezing—Reptiles and amphibians can be euthanized by rapid freezing when it
results in immediate death. Based on rodent models, it is likely that this can be achieved by
placing animals < 4 g (0.1 oz) in liquid N2.
52 The technique should not be used for species
that have adapted freeze tolerance strategies, as this method may not result in instant
death.607 Placement of animals ≥ 4 g in liquid N2 or other uses of hypothermia are not
acceptable"
Since none of us has liquid nitrogen, I don't think this is helpful, however it DOES say that "...other uses of hypothermia are not acceptable."
This is something I'm very interested in. I take in sick and injured turtles and tortoises all the time. Some are too far gone to keep alive. I feel that the refrigerator method - place the turtle/tortoise in a sealed plastic tub and put the tub in the refrigerator. After the animal has cooled down, at least over night, place the now sleeping animal into the freezer.
Naturally, I call the vet out for animals too large to fit into the fridge.
If anyone has a better method I'm all ears. It's all about being humane. I don't want to cause any more pain and suffering than the animal is already going through, and funds are limited as to how often I can call out a vet to take care of euthanasia.