Remove eggs from the refrigerator and let them come closer to room temperature by sitting them in warm (not hot) tap water for 5 minutes.
Place the 6 eggs in a single layer in a saucepan and cover with cold water by about 1 inch. Bring the water to a rolling boil over medium-high heat. As soon as it reaches a boil, remove the pan from the heat, cover, and let the eggs sit in the hot water for 10 minutes.
Meanwhile, prepare an ice bath (bowl of cold water with ice). When the 10 minutes are up, transfer the eggs to the ice bath and cool until completely cold, about 5 minutes. This stops cooking and makes peeling easier.
While the eggs are cooling, prepare the green onions: use only the green ends of the 4 green onions. Thinly slice the green ends; finely mince about 2 tablespoons of those sliced green onions for the filling and reserve the remaining thin slices for garnish. Set the reserved garnish slices aside.
Ensure the 1/2 cup small frozen shrimp are fully thawed. If still partially frozen, run them under cold water or microwave briefly on low in 5–10 second bursts until thawed. Pat the shrimp dry with paper towel, then finely chop them.
If you are using wasabi powder instead of paste, rehydrate now by mixing 2 tsp. wasabi powder with about 4 tsp. water to make a paste. In a small bowl, put the 3 T mayo and add the 2 tsp. wasabi paste in small increments, tasting as you go; stop when the mayo-wasabi reaches your desired heat level.
Peel the cooled eggs and cut each egg in half lengthwise. Remove all yolks and put the yolks into a medium bowl. If any egg white halves are badly mangled during peeling, set those aside or discard.
Mash the egg yolks with a fork until crumbly. Add the mayo-wasabi mixture, the finely minced green onion (about 2 T), the chopped shrimp, and a pinch of salt. Stir or mash until the filling is well combined and relatively smooth.
Transfer the yolk mixture to a piping bag or a small plastic bag with one corner snipped off, or use a small spoon. Pipe or spoon the mixture into the egg white halves, dividing it evenly among the halves.
Garnish each filled egg with the reserved thinly sliced green onion. Serve immediately or chill until ready to serve.