Pick through it with your fingers to remove any cartilage.
Add the oil, mayonnaise, onion, jalapeño, tomatoes, cilantro, and lime zest and juice to the crabmeat.
Using a rubber spatula or spoon, gently fold (or toss) all ingredients until well blended.
Season well with salt and pepper.
Top each tostada shell with a few slices of avocado, place a generous serving of the crabmeat mixture over it, and garnish with a sprig of cilantro. Serve each with a lime wedge.
Another more casual option is to put the crabmeat mixture in a bowl or platter and serve the tortillas alongside, allowing your guests to make their own tostadas. In this case, dice the avocado and fold it into the crabmeat mixture.