Have you sewn with "fur" before? It is notoriously difficult to handle! Satin binding can be rather difficult to sew on without ripples too. You may need to lift the presser foot every few inches to relieve distortion while you sew.
I would tie or tack the two pieces together, maybe every 4 to 6 inches, just to make sure they don't flop apart. I would do this by machine except the fur may not respond well to machine tacking, in which case I would hand-tack.