Hi Emma,
You don't trust the transcriptions, probably done by computer?
The Baptism was in Sønder Hygum, Haderslev, Danmark.
The confirmation was in Hygum Sogn (Haderslev Amt) (Hygum), Multiple, Danmark (Denmark)
Both in the same place, so logical that birth was nearby as well. Both of those are Denmark church records. From the Wikipedia article mentioned by George, the "Germanization" of the area was not very successful, esp. in the northern part of Schleswig-Holstein, where Sonder Hygum is located. However, Prussen is technically the correct listing for 1870 birth. Whichever you decide to use, I would put a note that the family was Danish and the records are Danish and that the area changed jurisdiction to Prussia during that timeframe.
Somebody did a lot of work to tie those references to the same person, sorting through hundreds of Hans Christian Hansens...