What causes wool to felt and shrink is the shock to the fibers from the change in temp from hot water to cold water, along with agitation with soap. When I was felting sweaters, I would wash them in hot water, and then stop the washer, fish out a sweater, wring it out as much as I could, and plunge it into a bucket of ice water. Repeat til water is all luke warm, and you are exhausted, lol. You can also just send it through a number of hot and cold cycles. You pretty much do just the opposite of what you do when you wash a sweater you want to keep wearing forever. Handle roughly, shock with temp changes, harsh soap, dry on high instead of flat. It's kind of fun after many years of babying cashmere sweaters.
Also, you don't have a problem with your petting. I mean, its kind of like a lamb, just flatter. I'm sure that fabric has a beautiful 'hand.' Are you sure you don't want to make a skirt or a pair of pants? They're really nice in cold weather... Edit: Oh, nevermind, as Rosanne Rosannadanna used to say. I saw that it was only a meter. Shrink away with impunity, friend!!