Picking it up is a good way to get bitten -- and mice do carry diseases. I had to handle mice a few times in the lab (one of the reasons I switched from lab research to epidemiology), and you had to hold them at the base of the tail between your pinky/ring finger and the scruff of the neck with your thumb/forefinger -- otherwise you'd get scratched or bitten. Bites hurt! I only got bitten once, and it didn't even break the skin (or the glove), but it left twin, deep bruises on my finger for over a week -- holding a pencil hurt for 3 days afterwards.
From personal observation, I would not call suffocating a "humane" method of disposal. The lab disposed of "excess" mice by dropping them in a CO2 chamber, and they would jump and twitch horribly before dying -- although this method has been determined by the AVMA to cause "no evident stress" to rats (
p.11 here). Of course, the CO2 accelerates death and acts as an anesthetic; suffocation without an accelerant or anesthetic does cause suffering.
From the same AVMA article, acceptable methods for euthanizing small rodents include "Barbiturates, inhalant anesthetics, CO2, CO, potassium chloride in conjunction with general anesthesia, microwave irradiation." "Conditionally acceptable" methods include Methoxyflurane, ether, N2, Ar, cervical dislocation (rats < 200 g), decapitation."
All of these methods require training and access to specialized drugs and/or equipment in order to use properly. Personally, I'd just drop it outside somewhere. Unless you have a friend with a pet snake that needs feeding soon...