Trim ends of zucchini; use a mandoline on the thinnest setting to cut zucchini into 1/8-inch slices. Place slices on a plate lined with paper towels, top with additional paper towels, and press down to remove excess moisture.
Place zucchini slices on a cutting board and lightly mist with cooking spray. Turn slices over and sprinkle with taco seasoning; lightly mist this side with cooking spray as well. Place slices seasoned-side up on a microwave-safe plate, making sure none are overlapping. Cook in the microwave on high power for 2 minutes and 30 seconds. Carefully flip slices over and cook 30 seconds more. Repeat with remaining zucchini.
Divide chips between 2 microwave-safe plates. Add black olives, red onion, jalapeno peppers, and Cheddar cheese. Microwave on high power until cheese is melted, about 30 seconds.