Place sliced cucumbers in a colander and sprinkle with 1 teaspoon salt. Toss gently and let drain for 15 minutes to remove excess moisture.
While cucumbers drain, in a large mixing bowl, combine Greek yogurt, lemon juice, black pepper, and garlic powder. Whisk until smooth.
Gently fold the crab meat into the yogurt mixture, being careful not to break up the lumps too much.
Rinse the salted cucumbers under cold water and pat very dry with paper towels or a clean kitchen towel.
Add the drained cucumbers, chopped red onion, and fresh dill to the crab mixture. Fold everything together gently until evenly combined.
Cover and refrigerate for at least 30 minutes to allow flavors to meld. Taste and adjust seasoning if needed before serving.
Serve chilled with lemon wedges on the side for squeezing over individual portions.