To make the zucchini water: Grate the zucchini on the large holes of a box grater and put it in a fine mesh sieve over a bowl; sprinkle with a pinch of salt and let stand for 15 minutes. Press the zucchini to extract as much water as possible.
To make the cocktail: Put the simple syrup, zucchini water, sake, and gin in a cocktail shaker filled with ice. Shake well and strain into 2 chilled martini glasses. Float a zucchini slice in each drink and serve immediately.
Put the sugar and water in a small saucepan and bring to a simmer over medium heat; stir until sugar is completely dissolved. Cool and transfer to an airtight container. Syrup can be stored in the refrigerator for up to 1 month.