Peel the shrimp and devein, reserving the shells. Toss the shelled, deveined shrimp in a bowl with 1 tsp kosher salt and the baking soda and let sit for 15 minutes while you prepare the poaching liquid.
In a pot, add the shrimp shells, lemon halves, the onion, celery, garlic, and bay leaf. Cover with water and bring to a rapid simmer over medium-high heat, then turn the heat down to low. Simmer over low for 10-15 minutes, then strain out and discard the solids. Keep the poaching liquid at a simmer over low.
Take the shrimp from the fridge and rinse. Turn the heat up to medium and add the shrimp and gently poach until firm, opaque, and cooked through. You don’t need to bring the poaching liquid up to a boil - it’s best if it’s barely simmering.
When the shrimp are cooked through, use a slotted spoon to scoop out the shrimp in a single layer on to a plate or rimmed baking sheet. Chill in the fridge.
While the shrimp is chilling, mix up the cocktail sauce. In a bowl, stir together the ketchup, chili sauce, horseradish, sugar, lemon juice, and lemon zest. Taste and adjust with salt and pepper. Spoon into a small bowl for serving.
When the shrimp are completely chilled, serve on a plate with lemon wedges and the cocktail sauce. Enjoy!