Preheat the oven to 450 degrees F (230 degrees C). Prick potatoes several times with a fork and place onto a baking sheet.
Bake in the preheated oven until potatoes are easily pierced with a fork, 50 minutes to 1 hour. Remove from the oven and let sit until cool enough to handle, about 30 minutes.
Slice off the top 1/3 of each baked potato. Use a spoon to scoop out all of the pulp from the potatoes and the tops, and place in a large mixing bowl. Set the emptied potato shells and tops onto a baking sheet.
Add softened butter to the potato pulp; mix on medium to high speed until well combined. Then blend in sour cream, salt, and pepper.
Roughly chop all but 4 shrimp. Stir chopped shrimp into the potato mixture with the Cheddar cheese until combined, then spoon it into the potato shells, molding it high. Add any overflow that won't fit into the top pieces. Slice 4 remaining shrimp in half lengthwise and arrange 2 pieces on top of each filled potato.
Bake in the preheated oven until cheese is melted, filling is heated through, and top is lightly browned, 20 to 25 minutes.