A method and an apparatus for applying an anesthetic includes a receptacle having an upper end, a substantially hollow interior, a lower end having a tube or nozzle extending therefrom and an attachment for attaching to the barrel of a syringe or vice versa. The receptacle receives a container or canister containing an endothermic gas or vapor (propellant) that rapidly absorbs heat when released to the atmosphere. A depressible actuating member or trigger propels the gas or vapor through an outlet nozzle that is oriented to project a stream of gas or vapor along a delivery axis that intersects a delivery axis of the needle; therefore, the gas or vapor can be successively delivered to an injection site with minimal repositioning of the housing.