Place 1 cup water and 3 cups of the Bloody Mary mix in a large saucepan; bring to a boil over high. Remove from heat. Add shrimp; cover and let stand until shrimp are barely opaque in centers, about 8 minutes. Immediately stir ice into shrimp mixture to stop cooking; let stand until shrimp are cool, about 5 minutes. Drain shrimp and pat dry.
Stir together cocktail sauce, vodka oil, lemon juice, hot sauce, Worcestershire, celery seeds, pepper, adn remaining 1 cup Bloody Mary mix in a large bowl or a large heavy-duty ziplock plastic freezer bag.
Stir shrimp, sliced celery, and onion into cocktail sauce mixture. Cover (or seal bag) and place in the refrigerator to marinate for at least 8 hours or, preferably, up to 24 hours.
Transfer shrimp mixture to a large serving bowl. Top with desired garnishes, and serve immediately. (The dish can be made in advance. Store, covered, in the refrigerator for up to 3 days.)