yes you do unfortunately have to remove the skins at least the free one you do when i get back ill see if the other one might fit.
UPDATE: it almost fit maybe if you have one of the thinner silicone cases it might fit, i have the black one made by nintendo so it has the grip lines on the side preventing it from going in, but it almost did if it wasnt for that.
PS i wouldnt say wasted you arent going to be playing all zapper games and you would have to take them off to change batteries any way. I will in the future have another controller for my zapper, and for other people when they come over.