Preheat the oven to 450°F and grease a baking sheet with cooking spray.
Season the crushed tortilla chips with the pepper, garlic powder, and cayenne. Taste and adjust the seasonings if needed, adding salt to taste. (Depending on the chips, I usually start with ¼ teaspoon.)
Lightly salt and pepper the shrimp then toss with the flour. (If using frozen shrimp that’s been thawed in cold water, pat down the shrimp with a paper towel before seasoning so they aren’t too wet.) Beat the eggs until bright yellow and place ½ cup of the crushed tortilla chips into a bowl. (You only start with 1/2 cup so you can refresh the chips as you dredge, which keeps them from becoming too clumpy.)
Working in batches, dip the flour-coated shrimp into the eggs then dredge in the tortilla chips. Place coated shrimp on the baking sheet. A quarter-way through the process, refresh the tortilla chip dredge with another ½ cup fresh crushed tortilla chips, then continue to dredge. Repeat the process until all the shrimp are coated.
Bake uncovered for 7 minutes, then remove the sheet from the oven and flip the shrimp over to the other side. Return to the oven and cook for 5-7 more minutes or until the coating is lightly browned and the shrimp are pink.
As they are baking, to make a chipotle cocktail sauce stir together the ketchup, horseradish, chipotle powder, and lime juice. Taste and add salt, if needed. After the shrimp are done, serve warm with the chipotle cocktail sauce and limes on the side.