Honestly? I think the heavy duty thread that comes with the speedy awl is what you want, not the fishline.
My father worked with leather for a living. When my awning stitching broke, I knew what he would have done - used some heavy duty upholstery thread, some wax (came in a thin block about the size of a matchbook) and two needles (one on each side of the thread) If there had not already been holes, he would have used an awl to make the holes, and then taken the double needle thread and gone put each needle through the hole - one going up, the other going down. The speedy awl does all that for you.
The reason I would not use fish line? It will break/rot more easily then the thread. There is a reason thread is used in the first place. I used heavy duty fish line to hang pics on my walls (because I have picture railing, and I liked how it was not very obvious) and I learned the hard way that you need to replace the line about every 5 years - or it will come crashing down in the middle of the night and scare the hell out of you.