Grate the peeled ginger over a bowl to collect one teaspoon.
Whisk the lime juice, sugar, and olive oil into the ginger.
Season with salt, pepper, and stir in half of the chopped mint.
Peel the melons, remove the seeds, and cut the flesh into chunks.
Peel and de-seed the cucumber, then cut into slightly smaller chunks than the melon.
Toss the melon and cucumber chunks together with the prepared dressing.
Trim the watercress stalks and add the leaves to the melon mixture.
Divide the salad between two plates, leaving excess dressing in the bowl.
Season the crabmeat with salt and pepper and pile it atop the salad.
Garnish with the remaining mint leaves and serve immediately.