I am not sure about sending the package to Denmark. When I send a package to Japan, I use USPS Global express/priority mail. The tracking tells you exactly where the package is. Leaving the port, the custom checking, leave for the local post office, received and signed.
You like to ship it as a gift. In this way, there is no import tax on the package, and most likely, no one checks the package. Usually, the package stays at the custom in the airport for 2-5 hrs. The Japanese post office delivers the express/priority mail during the weekend, so the total shipping time is about 4 days. The regular air mail is not. Again, I don't know about the Danish post office.
The USPS Global express/priority mail is insured up to $500 automatically when I send a package to Japan. This maybe the same for shipping to Denmark ??
Good luck !