I use Ezzox; brush it on with a small artist's brush. It gets dry yet leaves a tough lube film. Don't have to worry about it migrating to the wood, although it's not supposed to harm wood like oil or grease. Grease won't go anywhere though.
http://www.doublegunshop.com/forums/ubbthreads.php?ubb=showflat&Number=207576#Post207576I cleaned a boxlock used by the military in WWII. They put a pretty heave layer of grease inside and it never got to the wood. After almost 60 years, it was getting pretty dry.