For the shrimp: Preheat a grill or grill pan over medium-high heat.
Toss the shrimp with the olive oil and BBQ rub seasoning until evenly coated; set aside.
For the white BBQ sauce: Whisk together the mayonnaise, vinegar, horseradish, mustard, brown sugar, garlic powder and Worcestershire sauce. Stir in the chives and parsley. Season with salt and pepper.
Grill the shrimp until just cooked through, 2 to 3 minutes per side.
Divide the sauce among 4 martini glasses. Cut a small slit halfway through each lemon round and place 2 slices on the rim of each glass. Place 4 shrimp on the edge of each glass. Garnish with chives and parsley.