Well there are cultural irrelevancies in ahadith but this does not come from the Qur'an of course.
Another issue that is int he Qur'an on one hand is Surat Al-Baqarah ayat 34 "And when We said to the angels: Make obeisance to Adam they did obeisance, but Iblis (did it not). He refused and he was proud, and he was one of the unbelievers."
Surat al-Khaf "And when We said to the angels: Make obeisance to Adam; they made obeisance but Iblis (did it not). He was of the jinn, so he transgressed the commandment of his Lord. What! would you then take him and his offspring for friends rather than Me, and they are your enemies? Evil is (this) change for the unjust."
Shaytaan/Iblis is either a jinn or an angel. Does this not call for naskh
I believe there is no dispute among Muslims in that Iblis is not an Angel, the idea of fallen Angel is that of modern Christianity that is often confused. Islam doesn't teach that an Angel can commit bad deeds. An Angel as the Quran says had to be obedient having no option. I will paste below a quote from the Holy Quran proving that Angels are ever submissive to God.
[66:7] O ye who believe! save yourselves and your families from a Fire whose fuel is men and stones, over which are appointed angels, stern and severe, who disobey not Allah in what He commands them and do as they are commanded.
Before I address whether he was a Jinn I must once again point out that the Naksh and Munsook are only present in Islam today because of the loss of spirituality. Most Muslims today have left the Quran and only read it from the surface doing mouth worship towards. So now I will clarify the most common misunderstanding in trying to understand Jinn, a term that has evaded modern Muslims leading to birth of many fairy tales. I will quote below a passage from the book "Religion Rationality Knowledge and Truth" written by Hadrat Mirza Tahir Ahmad (ra) the fourth successor to the Promised Messiah (as).
Arabic lexicon mentions the following as the possible meanings of the word jinn. It literally means anything which has the connotation of concealment, invisibility, seclusion and remoteness. It also has the connotation of thick shades and dark shadows. That is why the word 'jannah' (from the same root word) is employed by the Quran to denote paradise, which would be full of thick, heavily shaded gardens. The word jinn is also applicable to snakes which habitually remain hidden from common view and live a life secluded from other animals in rock crevices and earthen holes. It is also applied to women who observe segregation and to such chieftains as keep their distance from the common people. The inhabitants of remote, inaccessible mountains are likewise referred to as jinn. Hence, anything which lies beyond the reach of common sight or is invisible to the unaided naked eye, could well be described by this word.
The Jinn
Hence Shaytan and Iblis can both be Jinn, and Angels by nature are Jinn. It is because Jinn is not a specific being, technically speaking any being that secludes from our eyes are also Jinn.
A clarification is also needed on the difference between Iblis and Shaytan. The word Shaytan is means something that is not good for you. For example the Holy Prophet (saw) said to cover open food as Shaytan will enter, he also said to not wipe your behinds with bones and lumps of dung as Jinn feast on them. In these instances it refers to microorganisms that are not good for us, something we better understand today. There could be no more suitable term to use in those times to describe microorganisms that are not visible to the naked eye.
Moving on to Iblis, this is a specific person who cause Adam (as) great harm. Whenever the story of Adam (as) is related specific mention is made of Iblis, which shows it is a particular person. He was in attribute Shaytan, as he took upon himself evil as his attribute, the way we may call a person a devil due to their tendency to engage in evil. But the name Iblis is for a specific human being, he can also be described as Jinn in the sense of being secluded or chieftain.