Little doubt

Once you put your wings on, is there no way to take them off without wearing another set instead? I mean, take off my holy wings without having to put the infernal ones.

No there's not a way to remove or unpack the wings. Either you use holy or inferno.

Do you mean without wings ?
If you already equiped either holy/inferno , then you can't. But you can feel that in hardcore mode . That's the only possibility !