Yes, spinning in the washer should be fine, just don't let it stretch. It may be easier to use the washing machine for all of it - put the blanket in, fill the tub and shut it off. Soak for a while, or hand wash it, then spin it out, you just need to avoid the agitation of the wash cycle. Woolite might not be good for it, I've heard that it can weaken the fibers. Use a little shampoo, and maybe a small amount of conditioner in the rinse.