Another hand washer here, in the bathtub with warm water and Woolite since I don't have a nice large laundry sink. Soak for a bit first, making sure everything gets thoroughly soaked. Some people swear by Orvus.
If you have one of those round laundry baskets with the holes in them (or get one at the dollar store), you can put the shawl in there and basically use it as an agitator drum. Lift out of the water in the basket, swirl around, etc. less pull on the fabric.
Rinse a bit in running water, then do a final soak in warm water making sure all the soap residue is out, that's often what makes old wool stiff. Squeeze the heck out of it, I get in the basket and do the grape stomping technique!. Do a final roll and press in a beach towel, you can help make the correct shape. If there is no overlap with the towel, put down a second one (basically a quilt of towel shawl towel). Then if you have one of those wood drying racks, this would be a good time to use it, you want plenty of support and plenty of airflow. I had an unused refrigerator rack that fit nicely over my bathtub and could dry things that way. Make sure it is completely and totally dry, maybe even air fluff in the drier a bit if everything seems stable.