Follow food processor manufacturer's instructions on setting up slicing blade. Set thickness to halfway and feed cucumbers into feed tube.
Set thickness to minimum and slice red onion using feed tube. Remove onions and cucumber to a large bowl.
In a separate smaller bowl, whisk the yogurt with the lemon juice and zest, salt, thyme, vinegars, and Dijon mustard.
When ready to serve, pour dressing over cucumbers and onions, toss to coat and top with crumbled feta. Serve immediately or wrap and refrigerate for up to four hours.