Peel the cucumber and cut into 4" pieces. Grate the outer flesh of the cucumber on the large grates of a box grater -- stop when you reach the cylinder of seeds in the center and rotate to a fleshier portion. Discard the seeds.
Transfer the cucumber to a fine mesh strainer set over a bowl. Transfer the shredded cucumber to the strainer and sprinkle with salt. Set aside.
On the small grates of the box grater, grate the knob of ginger. Scrape all of the ginger pulp into your (clean) hand and hold your hand over a small bowl. Squeeze the juice out of the ginger pulp - you should get about 1 1/2 teaspoons of ginger juice. Discard the pulp.
To the ginger juice, add garlic, sugar, rice wine vinegar, canola oil, sesame oil, lime zest, lime juice, salt and pepper. Stir to combine.
Press on the cucumber to remove most of the cucumber juice. Discard the juice. Transfer the shredded cucumber to the bowl and add the sliced onion and sesame seeds. Add 2-3 tablespoons of the dressing (you'll have leftovers - which can be used on another salad) and toss to combine. Serve.