If the 2 layers are separate, I'd risk it. I always wash knitwear that's dry clean only, using a weak solution of baby shampoo in just off cold water, then rinse in more cold water, spin in the machine and dry over the radiator or drape over the bannisters to dry flat.
I wouldn't risk it if the layers are attached; if the woolly layer shrinks at all, the whole garment will appear "buckled".
I'm grateful for your views - keeping it nice will be quite hard work I think and I wonder whether I'll ever really enjoy wearing it? I also wanted something that would keep me warm and with such little angora, I doubt it'll be particularly great.