Using a mandoline or vegetable peeler, slice zucchini lengthwise into thin ribbons, about 1/8 inch thick. Using a mandoline or chef's knife, thinly slice fennel bulb and shallot. Thinly slice chile peppers crosswise. Toss all slices with salt in a colander set over a bowl. Let stand 1 hour to release moisture.
Sandwich between layers of kitchen or paper towels. Press gently to absorb moisture. Transfer slices to a large heatproof bowl.
For brine: In a medium saucepan bring vinegars, sugar, mint, peppercorns, and coriander to boiling. Boil 2 minutes, stirring to dissolve sugar. Pour brine over slices. Stir in fennel fronds; let cool to room temperature.
Divide slices and brine equally among storage jars; top each with olive oil equally. Cure in refrigerator 24 hours before serving. Store in refrigerator up to 2 weeks.