Thanks for explaining. Now that I've taken time to explore the records that are readily available (I've posted some above) I definitely follow your logic!
Searching Dansk Demografisk Database (ddd.dda.dk) in Copenhagen in 1860s, not finding any Neuckranz, Neukranz, Neukrans, or similar. There's a Christian Neuckrans in Copenhagen in 1801 but he's a servant.
Here is a Kapt. Neucrantz in Fredericia, Denmark in 1751 and 1755:http://ddd.dda.dk/nygaard/visning_billed.asp?id=276750&s...
No Neukranz or Neuckranz turns up on ddd.dda.dk in Holsten (years before 1864) but there is a Neuckranz family in Sydslesvig in 1803 and in 1845, but no Ferdinand or Friedrich or August. (Note however that this is not a complete database.)