With that, I am assuming that when you say ham you mean ham that is salty tasting and typically pink in color. The word ham actually referrs to the part of the pig that a ham comes from-the butt, hip, or leg of the pig. Anyway, a fully cooked smoked (salty) ham should be good for at least a week in your fridge.Watch for signs of spoilage like a slime coating on the meat itself (not the fat), when in bright light-a metalic shiny substance usually green or silver in color (this is the beginning of mold), or a change in odor.he word ham actually referrs to the part of the pig that a ham comes from-the butt, hip, or leg of the pig. Anyway, a fully cooked smoked (salty) ham should be good for at least a week in your fridge.