Thinly slice the cucumbers and red onion using a sharp knife or mandoline.
Place sliced cucumbers and onion in a colander set over a bowl. Sprinkle with 1 teaspoon kosher salt and toss gently to coat. Let drain for 10 minutes to draw out excess moisture.
While vegetables drain, make the dressing: In a medium bowl, whisk together sour cream, white vinegar, sugar, and black pepper until smooth.
Pat the drained cucumber and onion slices dry with paper towels or a clean kitchen towel to remove as much moisture as possible.
Transfer dried vegetables to a large mixing bowl. Pour dressing over vegetables and add chopped fresh dill.
Gently fold everything together until cucumbers and onions are evenly coated with dressing.
Cover and refrigerate for at least 30 minutes before serving to allow flavors to meld.
Give the salad a gentle stir before serving. Taste and adjust seasoning with additional salt or pepper if needed.