Toast the chiles in a dry skillet over medium heat, turning often, until they soften slightly, about 1 minute. Transfer to a bowl and cover with hot water; let sit 15 minutes.
Transfer the chiles and 3 tablespoons of the soaking water to a blender. Add 1 1/2 tablespoons lime juice, 1 tablespoon vegetable oil, the garlic, oregano, cumin and 1/4 teaspoon each cayenne and salt; puree until almost smooth. Toss with the shrimp in a large bowl; refrigerate 15 to 30 minutes.
Meanwhile, heat about 1/4 inch vegetable oil in a medium skillet over medium-high heat. One at a time, fry the tortillas, turning once, until golden brown and crisp, about 1 minute. Remove to paper towels to drain.
Halve and pit the avocados; scoop the flesh into a bowl and mash. Mix in the scallion whites, 1 1/2 tablespoons lime juice, the remaining 1/4 teaspoon cayenne pepper, the cilantro and 1/2 teaspoon salt.
Heat the remaining 2 tablespoons vegetable oil in a large skillet over medium-high heat. Add the shrimp and cook, stirring occasionally, until just opaque, about 4 minutes. Season with salt and drizzle with the remaining 1/2 tablespoon lime juice.
Spread the mashed avocado mixture on the tostadas. Top with the shrimp, some sour cream and diced tomato, and the scallion greens. Serve with lime wedges.
Photograph by David Malosh
Recipe courtesy of Food Network Magazine