'No worries' is very informal, Australian English which has caught on in English speaking countries. Rather use 'Don't worry'.

I think you're overthinking it. People could use either one.

In my opinion, "Don't worry!" is correct in this situation and "no worries" is incorrect. "Don't worry" is a response to when someone is worrying, and you think it is unnecessary (hence you tell them not to worry). "No worries" is a response to when someone thinks they have done something wrong, and you are reassuring them that it is okay, that it's not a problem, etc. Example: A: "Sorry I am late!" -> '늦어서 미안합니다' B: "No worries" -> '괜찮아요.' / '아무것도 아니에요'