Just found these paddles on eBay. They look promising and feature a low price typical of Chinese ham gear.
http://www.ebay.com/itm/New-UNI-730A-Key-body-automatically-Mini-on-the-CW-Morse-Code-Keyer-Key-/121285138675?pt=LH_DefaultDomain_0&hash=item1c3d2858f3 (http://www.ebay.com/itm/New-UNI-730A-Key-body-automatically-Mini-on-the-CW-Morse-Code-Keyer-Key-/121285138675?pt=LH_DefaultDomain_0&hash=item1c3d2858f3)
I've seen these on Ebay before. They seem well built. American Morse also has small paddles for relatively low prices.. I love the Palm Mini Paddle I stuck on the side of my KX3.. That one would work great on a KX1 as well.
Gil.