Bring a medium pot of well-salted water to a boil and set a big bowl of ice water near the stovetop. Line a rimmed baking sheet with a clean kitchen towel.
Pull the strings off the sugar snap peas, then halve them crosswise. Trim the ends off the green beans. Boil the beans and peas until bright green but still very snappy, about 2 minutes, then drain and submerge in the ice bath to stop the cooking. Let cool. Drain, then spread over the prepared baking sheet and pat dry.
Cut Pecorino and salami into 1/4-inch pieces (you should have about 2/3 cup cheese and 1/3 cup salami, give or take). Combine beans and peas in a large serving bowl, season with salt and pepper, then add the cheese and salami.
In a small bowl, whisk together both vinegars and the oil; season with salt, pepper, and the sugar. Pour the dressing over the salad and toss to coat. Strip the oregano leaves over the top before serving.