To many historians, Brunkeberg marks a (if not the) deciding moment in the history of the Kalmar Union, so it's an interesting question.
The battle itself is rife with PODs. Like you yourself mention, if Christian I avoided getting shot in the face and instead slew Knud Posse, the leader of the Swedish detachment attacking from Stockholm, the unionists might very well have carried the day. The Sture Chronicle states:
"... and when it was eleven in the day, Sir Sten quietly came forward and immediately struck at King Christian's men, who were near the Monastery of Saint Clara [...] the King came to their aid, and Sir Sten Sture had to withdraw when Sir Niels Sture came to his aid ... and a multitude of men came out of Stockholm, led by Knud Posse. Then they once again struck the king on all sides and Knud Posse fought so hard that he came so close to the King that the King himself grievously injured him. Then the king was shot through the mouth and lost some teeth from a bullet fired from an arquebus."
Brunkeberg is important because it marked a changing point in the nature of the internal struggle between the Nordic realms. Hitherto, it had been a constitutional battle between crown and aristocracy, but the Sture stewards who seized Sweden after the battle, propagandised their victory as a national victory. So a Danish victory at Brunkeberg would most probably put a dent in that development. It's important to note that Christian's army contained considerable Swedish elements. Many members of the aristocracy fought for the king and the royalist peasants of Uppland probably suffered the most casualties of the battle. Furthermore, the principle of the union survived even after Brunkeberg, albeit the king gave up on his idea of enforcing it by military means in favour of cooperating with the council constitutionalists in the three realms. On the other hand, Christian's enfeoffment policy in Denmark gave even his most ardent Swedish supporters cause for concern, so we might see continued resistance as well. The most important development, IMHO, would probably be the culling of the border magnates such as the powerful Axelsons (Thott), who pretty much had conducted their own union policy separate from the royalists and council constitutionalists and caused Christian as well as the Stures a lot of grief.
In regards to foreign policy, Christian I (like his son and grandson), more or less continued the trade policies of Eric of Pomerania. He sought to combat Hanseatic influence and instead supported native tradesmen as well as the Hanseatic Dutch and English rivals. Although Christian had granted the Lübeckers substantial concessions in 1455, he did so in order to cut off their support to the Swedish rebels under Karl Knutsson. With Sweden secured, I think it likely that he would seek to break the Hanseatic hold on trade in the Baltic
