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".