I understand that No-Eyed sounds like doe-eyed, but that doesn't make it a pun because— A) Something without eyes cannot be doe-eyed. B) Describing a deer as having the eyes of a deer is tautological; you describe other things as being doe-eyed, not deer themselves.
The deer is no-eyed, it isn't being described as doe eyed. So your "A" argument doesn't apply here.
It may be poor wording to say deer are called doe-eyed, feel free to update the wording. Maybe pun isn't the right word either. However, it makes more sense, as normal deer are doe-eyed (by tautology), and DS deer are no-eyed, referencing their lack of eyes and the normal deer. "No idea" does not make sense in the context, it also has zero supporting arguments for why that would be the intended reference, as opposed to doe-eyed, which is very obvious and direct.