Preheat a grill or grill pan to medium-high. In a fine-mesh strainer, toss the cucumbers with 1 teaspoon of the salt and drain over a bowl for 15 minutes. In a small bowl, dissolve the sugar in the vinegar.
In a medium bowl, combine the remaining 1/2 teaspoon of salt, the lemon zest, 1 teaspoon of the dill, the Tabasco sauce and the olive oil. Toss the shrimp in the seasoned oil and set aside.
Squeeze the drained cucumbers to release extra water, then place in a dry bowl and toss with the sweetened vinegar. Mix in the yogurt and the remaining 1/4 cup of dill and refrigerate.
Grill the shrimp until cooked through, about 3 minutes on each side. Serve the shrimp warm or at room temperature with the cold cucumber salad.