Cut the stem ends from the zucchini and grate on the large holes of a box grater. In a colander, toss the grated zucchini and the salt with your hands and squeeze the zucchini to remove most of its liquid. Remove more liquid by patting it with a paper towel.
In a large bowl, combine the zucchini, chicken, cheese, scallions, red pepper (if using) and hot sauce. Taste the mixture and add more salt and/or hot sauce if needed.