It seems to me that a silicone based grease would be more water resistant and less likely to gum. However, Lubriplate makes a very light (NLGI #1) lithium based grease in small tubes. I have gotten mine in automobile parts stores that carry Lubriplate.
In years past, greases made for wet applications were made with calcium, magnesium, or aluminum soaps. Those soaps, unlike their lithium analogs, are relatively insoluble in water. Such a grease might be found in a grease made for use in boat trailer bearings or water pumps.