Good afternoon.
I do live in Düsseldorf.
You should get a green placard without any issues. The green one allows you to move your car within the entire city.
If you 'forget' to apply for the emission certificate the fine is 80,00 € + processing fees. Total will be 120,00 € ish.
You can order the placard online even without having a permanent residence in Germany. Link attached (I hope that works).
https://formulare.duesseldorf.de/metaform/Form-Solutions/?2&releaseUserId=05111000-0001-0041&allowedLanguages&releaseID=61e583a7f5d43b481498167f&releaseOrganizationID=05111000-0001&assistant=KFAS_AS_NW122624_FIM&storable=false&fileUrl=https%253A%252F%252Fformulare.duesseldorf.de%252Fmetaform%252FForm-Solutions%252Fsid%252Fassistant%252F61e583a7f5d43b481498167f&oID=05111000-0001&kdnr=05111000-0001
