Catherine de Valois of Burgundy dies in 1403, her husband Leopold IV (Duke of Austria) remarry a few years later, the bride is Catherine of Pomerania-Stolp sister of Erik of Pommern (King of Denmark), in OTL she married Johan, Count of Pfalz-Neumarkt, gave birth to Christopher of Bavaria (King of Denmark), before Leopolds death in 1411 (at age forty, so he's young enough to remarry) she give birth to a boy, let's call him Albert. Just like Christopher he's called to Denmark in 1439 to replace Erik, but here's the comparison end, Albert I of Denmark survive long enough to father a son and seing him become adult, and when he dies Albert is crowned King as the second Habsburg King of Denmark (and Sweden and Norway)*. Voila the Habsburgs is Kings of Denmark.
*This is the first time since in almost two centuries a clear succesion happen, when that happen for the Oldenburgs they stayed in power to today.