Chill the finely diced melons. Put cucumber, lemon juice, chile, and 2 tbsp. water in a blender and purée. Strain and chill for at least 1 hour and up to 1 day.
Tip out most but not all of the liquor from each oyster and nestle each into a cucumber round. Spoon some diced melon on top and some cucumber water. Top with cilantro.