Adjust blade of slicer to 1/8-inch-thick setting. Using slicer, cut each cucumber lengthwise into long 1/8-inch-thick julienne strips, slicing until you reach core, then rotate cucumber a quarter turn and continue slicing and rotating until left with nothing but core. Blanch cucumber "noodles" in a 4-quart pot of boiling salted water 1 minute, then drain in a colander. Immerse colander with cucumbers in a large bowl of ice and cold water to stop cooking, about 2 minutes.
Drain cucumbers, then transfer to a clean kitchen towel and pat cucumbers dry.
Heat butter in a 10-inch heavy skillet over moderate heat until foam subsides, then cook cucumbers, mint, salt, pepper, zest, and lemon juice, tossing to coat, until just heated through, about 1 minute.
