I've never seen a small flat mixer that fit into 1U when it was on a rack tray. It turns into 2U from the bottom of the tray up, and then depending on your tray, you may lose the ability to put anything below the tray.
You might consider a Mackie or other decent
small mixer board on a single space, roll-out rack
tray. Personally, wouldn't bother with the single space rack units.