Best way to splice together 20/22 gauge wiring?
3M Scotchlok's would work for this application.  They too would require a trip to a store, but the nice part is you don't need to strip the wire as they are self-piercing.  They can connect two or three wires, and are filled with a sealant to provide moisture resistance.

They are typically used for Telco wiring, but support wire gauge from 26-19AWG.