Step 1

Scoop 8 cups ice into a large bowl; set aside. Combine salt, sugar, and 6 cups water in a large saucepan. Cut lemons in half, squeeze juice into pot, and toss in lemon halves. Bring liquid to a boil, stirring to dissolve salt and sugar, then remove pot from heat. Add shrimp and poach, uncovered, 3½ minutes.

Step 2

Immediately add reserved ice to saucepan to rapidly chill the liquid and stop the cooking. Let shrimp sit in ice bath 10 minutes. Drain, pat dry, and peel. Pat dry again. Cover and chill until ready to serve.

Step 3

Do Ahead: Shrimp can be poached and peeled 1 day ahead. Keep chilled.

Step 4

Mix chili sauce, lemon zest, lemon juice, horseradish, pepper, and hot sauce in a small bowl. Cover and chill until ready to serve.

Step 5

Serve shrimp on cracked ice with lemon wedges and cocktail sauce alongside.

Step 6

Do Ahead: Sauce can be made up to 1 day ahead. Keep chilled.