I am not sure I would use the Double Loop stich on those. You will leave a stich line sticking up, making it somewhat uncomfortable as a handle. I think I would lace it the same as I would a pair of shoes, using latigo lace, pulling tightly as I go, so that the two edges butt up against each other. If you also use a little water to keep things damp as you go, it will dry even more tightly as it drys and shrinks. If you don't like the latigo....maybe your best bet would be hand stiching with thread.
Double Loop is best for items "Stacked" together like a wallet edge.