On 11 August 1633, while at a meeting in Schweidnitz (modern-day Świdnica, Poland), Ulrik was shot by an imperial horseman, and died the following day.
Thanks to the information in Grantville's histories, Ulrik's fate in the OTL was known well in advance, and he was able to avoid it. In 1633, he was traveling, officially incognito, on behalf of his father. In August of 1633, that took him to Grantville. While there, he had been able to visit the town's libraries, and had even been allowed to examine the personal library of one of the residents. He realized that, while there was a fair amount of information about his father, Christian IV, there wasn't much about the history of Denmark itself, as it was not a significant player in later centuries. He remained in Grantville until October of 1633, after which he went to Magdeburg, and then to Schwerin. While in Magdeburg, he saw the American ironclads, which were under construction, and thought they were formidable looking.
In January of 1634, Christian IV called him back to Denmark, and placed him in charge of researching and producing new, more effective weapons, a project which had already started under the Norwegian adventurer and tech-whiz Baldur Norddahl. The two men quickly became fast friends. Ulrik also befriended American Eddie Cantrell, who had been captured at the Battle of Wismar.
While he was willing to work on the weapons projects, or at least keep his father out of the way while Baldur worked on spar torpedoes and mines, he was opposed to his father's decision to join the League of Ostend and remain in it. Not only was he aware of American technology and what it could do, he expected that Denmark would bear the brunt of any USE response. During the Battle of Copenhagen, he and Baldur managed to disable the SSIM Monitor with a spar torpedo, though they only survived because the Monitor did not sink and took them aboard.
Following the end of the Ostend War, in the accords which annexed Denmark to the reconstituted Union of Kalmar, it was arranged for him to marry Kristina when she came of age. Ulrik didn't mind the betrothal not only because he was raised with the knowledge that he would marry for political reasons, but also Kristina's perceptiveness and intelligence at a young age banished his fears of marrying a dull woman.