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Wash the shrimp under cold running water.
For the brine, combine the 1/4 cup of salt and quart of water in a large mixing bowl and stir to dissolve the salt crystals. Squeeze 2 of the lemon wedges into the water and add the rinds as well. Add the shrimp and refrigerate for 15 to 20 minutes - no longer, or the shrimp will become too salty.
Meanwhile, make the sauce: Combine the dry mustard, Worcestershire sauce, A-1, and cream and whisk to blend. Whisk in the mayonnaise and salt and cayenne pepper. Cover and refrigerate until ready to serve.
Drain the shrimp, rinse under cold running water, and drain again. Pat dry with paper towels.
When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Set the temperature to 450F (High) and preheat, lid closed, for 10 to 15 minutes.
Arrange the shrimp on the grill grate and grill, turning once, 3 to 4 minutes per side, or until the shrimp is pink and opaque and cooked through. Transfer to a platter or plates and serve with the sauce.