Can Non-european Citizen living in Skåne Sweden go to Copenhagen Embassy to ask for a Chinese Visa?

Why don't you apply for a China visa in Stockholm, Sweden? You live in Sweden rather than Denmark, your application will be denied:

Applicants from the third countries who have obtained Danish residence/permanent residence permit can apply China visa in Denmark, one of the following documents needs to be presented besides above mentioned documents.
a.Copy of residence permit
b.Employment letter or Confirmation letter issued by the Danish company

Simply because Copenhagen is 30 minutes away by Train and Stockholm 5 hours. For one day service, this is more convenient.

Thierry, please apply for China visa in Stockholm. If you don't want to go to Stockholm in person, please send application to Chinese Visa Application Service Center by post, for more information, please refer to http://www.visaforchina.org/STH_EN/applybypost/index.shtml