Make the dressing. Combine the mayonnaise, celery leaves, 2 tablespoons chopped cilantro, 1 tablespoon water, 1/2 teaspoon salt and a few grinds of pepper in a large bowl. Grate in the zest of 1 lime and squeeze in the juice.
Toss the shrimp with the vegetable oil, 1/4 teaspoon salt and a few grinds of pepper in a bowl. Arrange the shrimp on the grill and cook until pink and just firm, about 2 minutes per side. Transfer to the bowl with the dressing; squeeze in the juice of the remaining 1/2 lime.
Add the sliced celery, avocados, salad mix and radishes to the bowl with the shrimp; toss to coat. Top with the remaining 1 tablespoon chopped cilantro.