Bring a pot of salted water to a boil. Turn off heat and add shrimp and cook for 3 to 5 minutes. Drain. When cool enough to handle, slice each shrimp in half lengthwise.
In a small bowl, whisk together the olive oil, ginger, lemongrass, lime zest and juice, and hot sauce. Season with salt and pepper. Set aside.
Halve the honeydew and watermelon, cut away from rind, and remove the seeds. Slice the melons into 1/8-inch-thick pieces. Remove the watermelon seeds (it's okay if the slices don't stay intact). Using a cake ring or a glass whose mouth is slightly smaller than a 14 to 16-ounce martini glass or champagne coupe, cut out 16 slices from the watermelon, and 16 slices from the honeydew. Save the best-looking 4 watermelon slices.
Set out 4 (8 to 12-ounce) martini glasses or Champagne coupes.
Layer 2 slices of watermelon and honeydew in each glass, lightly sprinkling each melon layer with the lemongrass dressing, chopped basil, chopped cilantro, salt, and pepper. (You may need to trim the melon slices so they fit neatly into the glasses, which should be half-full at this point.) Divide the shrimp among the glasses, arranging them in concentric circles. Season the shrimp with the dressing, basil, cilantro, salt, and pepper. Add another layer of melon in the reverse order: honeydew, then watermelon, seasoning as before. Top each salad with a reserved watermelon slice, and sprinkle lightly with the dressing, basil, cilantro, salt, and pepper. Garnish with 1 basil and 1 cilantro leaf. Refrigerate for at least 1 hour before serving (the melon and shrimp taste best when well chilled).