Ben,
I was looking for a small "paddle type" strop to chunk into my ditty bag for the purpose of keeping my straight razors in proper trim. Couldn't find one to fit my parameters of size/cost, so I set about making my own.
Started with an oak "scant board" 1/4" thick by 2" wide from Lowe's to form the paddle. To that I glued (Titebond II) vegetable tanned leather, grain (smooth) side up. Onto one of the pieces of leather I glued canvas (yes canvas), stretched it out tight and smooth, and once the glue dried, trimmed it off nice and flush all around the edges.
To prepare the strop for use, I loaded up the canvas side with Flexcut Gold, an extremely fine abrasive/polish available at stores that sell wood carving supplies (Wood Craft) or order off the internet. The smooth leather side of the strop I lathered up well with some of my shaving mug soap, working the lather into the leather, wiping off the excess, and letting it dry. Once dry, the fats, etc, in the soap allow you to polish the leather strop fairly slick using a smooth piece of glass like a bottle.
The whole rig, including handle, is only about eight inches long. Fits handily into my shaving kit, and keeps my straight razors shaving silky smooth. To make one suitable for stropping khuks, simply fashion a larger version of what I've described above. The most expensive component would be the Flexcut Gold, but one small brick of that stuff lasts a long, long, time.
Sarge