Preheat grill to medium, about 350 to 400 degrees F.
Rinse the tops of the mushrooms briefly under running water, rubbing off any debris, and pat dry. Gently remove the gills with a spoon (the gills are edible, but their dark shade can muck up the color of the filling). Pluck off the stems, trim the bottom of the stems, and reserve. Trim the rims of the mushrooms with kitchen shears, for a straighter edge. Reserve scraps. Place mushroom caps on a plate.
Slice finely slice enough of the green scallion tops to equal 2 tablespoons and reserve for garnish. Place the remaining white and green scallion parts in a large food processor and pulse to chop. Add the mushroom stems and scraps, shrimp, lemon zest and juice, and freshly ground black pepper to taste. Pulse until the shrimp is nearly ground, with some small pieces remaining.
Brush the mushroom tops with oil, turn them over, then sprinkle lightly with salt and pepper. Divide the shrimp mixture equally among the mushrooms and smooth with the back of a spoon. Sprinkle with salt.
Lightly oil the area of the grill that you will be using. Grill the stuffed mushrooms until the shrimp centers turn white and firm when pressed gently and the mushrooms are tender, about 10 to 12 minutes. Allow the mushrooms to rest a few minutes before serving. Sprinkle with sliced scallions and serve with lemon wedges.