Start by making the cocktail sauce since it needs no cooking and can be made while you prep other components. Whisk together the ketchup, horseradish, 2 tablespoons lemon juice, chili powder, hot sauce, and Worcestershire sauce in a small bowl until smooth. Set aside at room temperature. While the sauce rests, mince your garlic finely, zest both lemons (reserve the zest), juice one lemon if you haven't already, and chop your fresh parsley. Pat the shrimp completely dry with paper towels—this is crucial for getting a good sear on the grill.
Place 4 wooden skewers in a shallow dish and cover with water to soak for at least 30 minutes while you prepare the marinade (soaking prevents them from charring on the grill). In a medium bowl, combine the olive oil, lemon zest from Step 1, minced garlic, paprika, cayenne pepper, celery salt, and honey. Whisk until the honey dissolves and everything is well combined. This is your flavor base for the shrimp.
Add the dried shrimp from Step 1 to the garlic-lemon marinade from Step 2 and toss gently to coat evenly. Let them sit for 5 minutes to absorb the flavors—I find this brief marinating time makes a big difference in depth of flavor without making the shrimp mushy. Remove the soaked skewers from water and thread 5 shrimp onto each skewer, leaving a small space between each one so heat circulates evenly.
Heat your grill to high heat and lightly oil the grate to prevent sticking. Once hot, carefully place the skewered shrimp on the grill and cook for 3 minutes on the first side without moving them—this develops nice char marks. Flip each skewer and grill for another 2-3 minutes until the shrimp are opaque and cooked through. Watch carefully since shrimp cooks quickly and overcooking makes it tough and rubbery.
Remove the shrimp skewers from the grill and transfer to a serving platter. Garnish with the fresh parsley from Step 1 and arrange lemon wedges alongside for squeezing over the top. Serve the cocktail sauce from Step 1 on the side for dipping. The bright lemon and fresh garlic flavors are best enjoyed immediately while the shrimp are still warm.