I'm not familiar with that particular batting but does it have a scrim? If not, I would think it would be difficult (impossible?) to wash or machine dry. I personally have not pre-washed any of my bats, but once I doused it with water and dried it ... not so much for the shrinkage but to get the wrinkles out. That was a W&N bat.
If it has a scrim I would wet it while flat (in the tub perhaps) then dry it. I have a top load machine and I can't fathom the mess I would have if I machine washed it with an agitator (even on the "delicate cycle which agitates just a few turns then stops for a few minutes).
If it doesn't have a scrim ... I wouldn't wash or dry it.
5% is an awful lot, even for cotton.