I really doubt it. I know in humans the texture is defined by the hair follicle. Shaving wouldn't change the hair follicle. If you decide to do it and it works let us all know though.
You also might try a product called Cowboy Magic, Concentrated Detangler and Shine. You can see if a store is near you by going to their website
www.cowboymagic.com It is very good for cottony coats that matt.