Don't know how dense your strap is. I have sewn 4 layers of webbing with my computer machine -- 18 jeans needle, a 3 stitch, the jeans-a-ma-jig (to keep the presser foot level) and very slow speed. If it is more dense than the webbing you can use for bag handles, if you have non-computerized machine available, an 18 jeans needle and a jeans-a-ma-jig would probably get you through since the piece is not that wide. Otherwise I would go to a shoemaker.