As to the electric fence it is hard to say, remember they have a good layer of insulation in the form of feathers or down so they may not feel a thing if they touch it. On the other hand there is a goose control device on the market (to control Canada geese which are pests) that basically consist of two strands of string at just the right heights. Geese don't like to duck under things. Of course if the Canada really wants to go somewhere he just flies over it. We had this around a pond at work and the geese just flew in and out. It was partly effective because there was better pasture in the area and the geese would fly between the pasture and the pond, before the string they would walk out of the pond and graze our lawn, sit on our side walks and poop all over the place. The string job actually cut the poop problem by 68% (I got to count the poop and do the statistics)
Try a dog house with a high door (made for bigger breeds) like I said, geese don't like to duck under things.
