There is supposition that an affair between Frederick II and Anne Corfitzdatter Hardenbeg let to the possibility of child(ren) Catherine perhaps being one of them, but so far, there seems to be little or no documented proof of this.
Considering that Frederick II married Sophia of Mecklenburg Gustrow in 1572 on July 20th, and Catherine's birth was reported as on 8 Apr 1580 was he having an affair with a lost love during his marriage. Will we ever know??
"1573 Acting County Sheriff
Anne Corfitzdatter Hardenberg of Helsingborg (Sweden)
Of high nobility, she was chamber-maid to Queen Dorothea 1557-71, and here she got to know king Frederik II (king from 1559) who fell in love with her, and wanted to marry her, but this met widespread opposition. In 1572 she married Councillor of the Realm, Oluf Mouritsen Krognos, who died after only six months marriage. She lived at her dowry Bregentved and managed to keep her husband’s family at distance with the help of the royal family. She (d. 1589).
Malky
Excerpt from
http://www.guide2womenleaders.com/Governors.htm