The new-born Prince is to be Gabriel Carl Walther, Hertig (Duke) of Dalarna
. His arms will almost certainly be the same as those of the previous Duke:
Q3 are the arms of Dalarna.
The previous Duke was Prince Carl Johan Arthur
(1916-2012), youngest son, of King Gustaf VI Adolf and his first wife Princess Margaret of Connaught. He lost his rights as a prince in 1946 when he married morganatically. (If the same rules applied today, none of the King's children or grandchildren, including the Crown Princess, would be able to succeed to the throne.)
On 2 July 1951, for himself, his wife and his marital descendants, he was made Count of Wisborg in the nobility of Luxembourg by Grand Duchess Charlotte and took the name Carl Johan Arthur Prince Bernadotte. The Counts of Wisborg are considered to be part of the Swedish unintroduced nobility. As Count of Wisborg his arms were different, but still royal - both Vasa and Bernadotte:
The only previous Duke of Dalarna was Prince Nikolaus August of Sweden and Norway (1831-73), the youngest child of King Oscar I of Sweden and Norway and Josephine of Leuchtenberg. His arms were rather different, firstly because of the Norwegian element, secondly because the Dalarna element was not a quarter. Arms as an adult: