I can't speak to the use of a grease hole, but properly rendered animal fats shouldn't get smelly if they go off. Animal fats mixed with beeswax won't go rancid ever, I'd think.
I have arrows greased with lard that have been sitting around for months now, with no noticeable smell. I greased my rifle with lard and left some of the lard on it for five or six years, and it didn't stink - go red and then turn black, yes. Stink, no. I have a 50:50 mix of home-made tallow, not the best rendered stuff, that has been sitting around unrefrigerated for a decade or more, and it was fine the last time I checked.