You're right, I don't think there IS a right-size clip for this. I have an 18mm desktop too and the medium-sized clip (32mm wide) won't fit. If it DID fit, the lever part would be too big for most cables - they would drop right through.
So we need to be using the smaller clips - and that means a thinner (very thin) desktop. The only thing I can suggest is that you try using the BIGGEST clip to attach a piece of cardboard or plywood to the desk surface - then have the smallest clips on that piece of thin board to hold the cables.
EDIT: I was quite impressed with this that I just found on Google Images. I shows that the largest clips CAN be used but in a slightly different way:
To my experience these clips do not come in a great variety of sizes, which could give you a little problem. However as long as you have one which is too large it is simply a matter of attaching something beneath the surface to make it a better fit.
You could either fold up some paper or cardboard or even a strip of wood, and put this below the desk so it is not visible. This should make the standard sizes of clips an easy fit to your desk.