Leaving school and Japan, change visa?

Hello everyone,
I have been on a student visa for one year but I notified my school that I'll stop going to school as I will go back to my country in December.
The thing is I told them on the 15th of November and I'm leaving on the 20th of December, I already booked my plane tickets but they told me I have to change my visa to a temporary visa. ( or do the classic go to Korea weekend and come back )
My school said I only have the right to stay 2 weeks in Japan after they contact the immigration.

So... I would have to change my visa around the 30th of November ? Do I really have to or can I stay with my visa until I leave the country ? ( I mean if I could avoid immigration and more paperwork I'd like to as there's quite a lot of other things to do. )
Is it risky to wait until the immigration gets in touch with me about this matter ? ( If they do )
Thank you !

Your school is wrong. After they notify immigration, you can stay until yout status expires or immigration tells you to leave (by revoking your status).