Do you really need grease or will oil work just as well?
Buzz, grease is oil...suspended in a thick soap base to keep it in place.
A small amount of any good grease or oil will be fine to lubricate a shotgun hinge pin joint or knuckle. Oil is more likely to run off or soak into wood if you use too much. The main concern is that you have a film of good lube that is free of any abrasive dirt or contaminants. Most people should never run out of it since so little is needed. DimmyW might because he says he cleans his guns twice a week. I use Mobil synthetic grease, but have several other brands in the garage. Any would be fine.