Fill a 3- to 4-quart saucepan with water, then introduce the Old Bay, pickling spice if using, and squeeze in the juice from half a lemon, adding the lemon itself to the pot. Bring this seasoned water to a vigorous boil before gently placing the shrimp into the saucepan. Always retain the shells while cooking and do not devein beforehand. Allow the shrimp to simmer for 3 to 4 minutes, judging doneness by firmness rather than softness; if the pan is crowded, wait for the water to return to a boil and extend cooking by an additional 1–2 minutes if necessary. Once cooked, drain the shrimp immediately using a colander. Avoid plunging the shrimp into ice water, as rapid chilling diminishes their flavor. Instead, toss the hot shrimp with ice in a large bowl or the colander itself, permitting them to chill naturally for 5–7 minutes as the ice melts away. Once adequately cooled, peel and devein the shrimp. This step may be completed in advance, but do not cook the shrimp more than eight hours prior to serving. Present the chilled shrimp atop crushed ice, accompanied by fresh lemon wedges and the prepared cocktail sauce. For the sauce, thoroughly combine the ketchup, chili sauce, Worcestershire sauce, horseradish, and lemon juice in a small bowl, adjusting the horseradish quantity to your preferred level of heat. Keep chilled until ready to serve.