My machine has a wool wash cycle, I've always washed my wool suits on the coolest setting stretch back a little into shape to flatten, and hang to dry and they've been fine.
When I am doing a dry clean only item rather than put detergent in the ball in the machine I mix it with water in a jug and pour it in through the drawer as it fills then you don't get the risk of neat detergent on the fabric. I do this as the only prob I ever had washing a dry clean only jacket was a detergent stain on the edge of the velvet lapel.