There isn't a white or silver cape and you can get the one you need from battles. On the battle page scroll down to the bottom and you'll see 'battle for resources If you choose that and then choose storms Cape from the options it will show you all 6 of storms capes that are available, the ones you haven't collected before are the ones in white but press one of the white spaces and you can target it
You can battle for resources you haven't gotten from missions. I had to for the assassin's choker since none of the missions gave me the last one I needed. When you go to battle for resources just pick the box with static in it.