Is “nö” a regional thing? Last time I went to Germany I encountered far more people saying “nö” or “ne” than saying “nein”.
I totally agree that as a non-native-speaker one should stay on the formal side whenever in doubt.
But you should not understand every “nö” as respectless.
Often it is just less harsh than “nein”.
If I say to a student “Nein, …” she/he will understand it (hopefully) as “Nein, auf keinen Fall” whereas “Nö, …” will be more like “Nö, besser nich(t).”
I think that is a general feature of dialect: It tempers.
If I enter a lab and say: “Watt für’n Wuling hier.” (Wuling: Northern German for “chaos” from the Frisian seaman’s expression for an unsorted heap of rope), it will be a mild reproach. If I say the same in Hochdeutsch, the order to clean up will send students scrambling.
I’d like to add that I feel like this sentence in this form only works with “och nö”, and with the accompanying tone. On tatoeba there is also a more formal version: “Oh nein, sie schon wieder”, but that expresses a different feeling:
Oh nein, sie schon wieder -
Och nö, nicht die schon wieder -
Depending on the tone, the formal version can also be shifted towards “och nö”, but “och nö” is pretty unambiguous.