It's all so specific to the chair. My son's chair has a head rest, lateral supports, lots of straps that cross over the chest and waist -- so to create any kind of cover would be very cumbersome. Another key question would be who do you expect will be putting this cover on the chair and taking it off? Is she able to do that herself? Will ties be difficult for her to manipulate or to reach? I'd suggest using stitched in velcro-- the industrial strength type works very well, yet is easier to use than ties that might become very tight when stretched.
Another thing to be very careful about is avoiding anything that will result in big lumps or folds under or behind her -- depending on the individual's needs, lumps can lead to skin breakdown.
I would think that a natural fiber batting would help most with sweat. One of the favorites with wheel chair users is having a sheep skin liner-- wicks moisture, is soft, and yet warm (cause vinyl is horrid in cold weather too). If she has a custom wheelchair, she can request a different material for her seating system next time. She may even qualify for an upgrade now-- something to check in her medical coverage.