I agree with the others about the Velcro. My thinking is that unless you make them short enough they could get tangled up on the wheels. One other thing my might want to add, depending on how you design it is adding a pocket or two. I spent 4+ months in a w/chair a few years ago and would have loved to have had some kind of pocket or holder to put papers, snack, book, etc in would have been so helpful. I finally had my husband buy a nail apron at the hardware store and tied it to the side of my w/c. Big help.
Anyway just a thought. I totally get where she is coming from about sweating. That vinyl gets very hot and sticky. You are a good friend to do this for her. God bless you for all your efforts.