I work with mice and rats everyday and we have to follow laws/rules/guidelines, including the AVMA (American Veterinary Medical Association) guidelines for euthanasia. Here's a little excerpt talking specifically about neonates/5 days and younger pinkies.
S2.2.4.2.2 Physical Methods
Hypothermia—The gradual cooling of fetuses and altricial neonates is acceptable with conditions. As cold surfaces can cause tissue damage and presumably pain, the animals should not come in direct contact with ice or precooled surfaces. Hypothermia for anesthesia is not recommended after approximately 7 days of age. Therefore, it is also an unacceptable euthanasia method in animals older than this age. Fetuses that are believed to be unconscious and altricial neonates < 5 days of age that do not have sufficient nervous system development to perceive pain may be quickly killed by rapidly freezing in liquid N2.
Decapitation—Decapitation using scissors or sharp blades is acceptable with conditions for altricial neonates (< 7 days of age). Some rodent neonates, whether atricial or precocial, may have a tissue mass that is too large for some scissors. Consideration should be given to the potential of pain from tissue crushing as well as to personnel safety. When appropriate, another method should be selected or an adult decapitator used.
Cervical dislocation—Cervical dislocation by pinching and disrupting the spinal cord in the high cervical region is acceptable with conditions for fetal and neonatal mice and rats.