In a medium bowl, stir together the crabmeat, celeriac, lime mayonnaise, chiles, and salt. Taste and add more salt if needed. Divide the crab salad among the tostadas, spreading it in an even layer. Top each tostada with the avocado slices and sprouts and serve with the lime wedges.
How to make homemade tostada shells (optional): In a large deep-sided pot, heat 2 cups safflower oil over medium heat until 350 °. Fry 6-inch corn tortillas, one at a time, for about 2 minutes each, or until golden. While frying, hold down edges of tortilla with two forks to keep the tortilla flat. Drain tortillas on paper towels. Let cool for at least 15 minutes.