To make the dressing, peel the ginger and grate it over a bowl - you should get about a heaped teaspoon.
Using a small whisk (if you have one - otherwise stir with a spoon), combine the lime juice, sugar and olive oil with the ginger.
Season with a little salt and a generous grinding of black pepper. Roughly chop the mint leaves and stir half of them in.
For the salad, peel the melons, cut the flesh in half and scrape out the seeds with a teaspoon. Cut the flesh into chunks.
Peel the cucumber, remove the seeds and cut the flesh into chunks, slightly smaller than those of the melon.
In a bowl, toss the melon and cucumber together with the dressing.
Trim only the toughest stalks fromf the watercress and add it to the melon.
Divide the melon and watercress between two large plates or salad bowls, leaving any extra dressing behind in the bowl.
Season the crabmeat with a little salt and black pepper. Pile the crab on top of the melon and watercress.
Scatter over the remaining mint leaves. Serve straightaway.