Toast the chiles in a dry skillet over medium heat, turning often, until they soften slightly, about 1 minute. Transfer to a small 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 of the lime juice, 1 tablespoon of the vegetable oil, the garlic, oregano, cumin and 1/4 teaspoon each of the 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, flipping 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 of the 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.