Another good resource is the Danish emigrant database, so many young Danes were leaving Denmark in the period after Denmark lost the war with Germany in the 1860s that Denmark started this database and it has been online for over a decade. It lists emigrants from Denmark from 1869 to 1908 and is part of a larger database of pay for view databases, but since so much of the Danish records are on film at Salt Lake City I would start with those records first.
Here is the URL for the emigrant database: http://primary-sources.eui.eu/website/danish-emigrant-database
There was a universal draft of 17 year old males and they registered the males at birth and then every 2 to 3 years after that. Those records are on microfilm also, and you will find a lot of 16 year old males leaving Denmark on the emigrant database.