Make the slaw: Mix the mayonnaise, relish and lemon juice in a large bowl. Add the coleslaw mix and scallions; season with salt and pepper and toss to coat. Cover and refrigerate until ready to serve.
Fill a large bowl halfway with ice water and 1 tablespoon salt. Butterfly the shrimp: Make a deep cut down the back of each shrimp so it can be splayed open. Soak in the ice water, 5 to 10 minutes.
Meanwhile, place the saltines in a large resealable plastic bag and finely crush with a rolling pin; transfer to a bowl. Mix the flour and Old Bay Seasoning in another bowl. Lightly beat the eggs in a third bowl. Dredge the shrimp in the seasoned flour, dip in the eggs and press into the crushed crackers, splaying each one open to coat inside the incision. Transfer to a plate, cover and refrigerate until ready to fry.
Heat 3/4 inch vegetable oil in a large heavy-bottomed skillet over high heat until a deep-fry thermometer registers 350 degrees F. Fry the shrimp in batches, turning once, until golden, 1 to 2 minutes. Drain on paper towels and season with salt. Serve with lemon wedges and the slaw.