I wouldn't pre-wash a batting if the packaging didn't give instructions for doing so. As I recall, Warm and Natural batting specifies not to spin it. That's what makes it hard to pre-wash, since you have to try and squeeze the excess water out by hand and with towels before putting in the dryer.
I wonder if washing the quilt in cold water and air drying the first time would eliminate the need to pre-wash the batting? Quilter's Dream says the shrinkage is minimal, and they specifically say pre-washing is not necessary, and don't give directions for it.