I would have assumed an 1865 merging of Denmark and Sweden-Norway would have been based around a POD in the Second Schleswig War. Christian XV had made promises regarding Sweden's aid. Not smart, but even a failed attempt to aid Denmark could have an effect. Or maybe the POD was actually like 1859, in that Christian XV started preparing the Swedish military for the Second Schleswig War from the beginning of his reign. However that would both affect the German Confederacy's views regarding the war if Sweden looked to be preparing to reinforce Denmark, but also likely force concessions on Denmark's side. Sweden would probably demand any buildup they undergo to be proportionally matched by Denmark, but Sweden also didn't want to get involved in a conflict with Germany in trying to keep Danish control of Holstein and the German parts of Schleswig. I'd assume any Swedish commitments to war would be accompanied by demands for Denmark to willingly give up Holstein alongside the German majority parts of Schleswig. Something like 'Sweden will fight for Scandinavia. Not Denmark's German fiefs.' This would be important as the Germans took even the ethnically Danish parts of Schleswig while promising to have plebiscites on whether they wanted to be part of Germany or Denmark, but never did it as the Austro-Prussian War really rewrote German policy. If Sweden either reinforced the Dannevirk or simply bailed Denmark out of trouble later while offering a peace that Holstein goes to Germany while plebiscites are held throughout Schleswig afterwards to decide the border between Denmark and Germany, it could have ended the war earlier or more amiably for nationals on both sides.
I didn't actually know there was any talk of Charles succeeding Frederick. Although not so sure how that would have turned out. Denmark and Sweden still followed Salic Law, and Charles only had a single surviving daughter. Meanwhile his brother, Oscar II, had married a German lady, not exactly a great marriage for the sole monarch of a united Scandinavia in this time of nationalism and scandinavianism. However Charles' daughter, Louise, had married Christian IX's heir, Frederick. They become King and Queen of the United Kingdom of Scandinavia, Christian IX willingly demotes to Grand Duke of Denmark, Oscar II becomes Grand Duke of Sweden, and Louise and Frederick's second son is to be named Grand Duke of Denmark while their first becomes king. Their third could then one day become Grand Duke of Norway.
Ah, who cares about that. Monarchs didn't exactly matter by that time anyways. Plus, I don't know enough about their succession laws, public opinion on pan-Scandinavianism, nor how even those supporters of Scandinavianism likely envisioned a political union playing out to make an accurate guess.
The devil is in the details, regarding the exact POD, the Second Schleswig War, and the exact political specifics of a united Scandinavia. Some general thoughts though. If Germany still claimed all of Schleswig, so a POD that doesn't alter the Second Schleswig War (maybe Christian IX's offer to join the German Confederacy if it could keep Schleswig and Holstein is leaked, and the people overthrow him and offer the throne to Charles XV) a united Scandinvia would be in a much better position to 'convince' Gemany to hold the plebiscites or Germany might face a revanchist Scandinavia for those areas of Schleswig dominated by Danes. You'd likely see a lot more militarization of the border with Germany. Denmark didn't want to serve as the southern watchdog of Scandinavia, for good reason, but a united Scandinavia would as a matter of course feel it necessary to build up their land border with the continent with soldiers from all over. Maybe their own Maginot Line as the new Dannevirk on the border. Otherwise I'd imagine such a state would adopt Sweden's armed neutrality, as it is right in the middle of three Great Powers in Germany, Russia, and Britain. I'd say it might lean a bit towards Britain though. Germany could at least be perceived as being manageable if they build up the land border enough. Meanwhile Scandinavia would have a better chance of matching Russia or Germany in naval matters in the Baltic than they would of matching Britain anywhere else. So a friendly relationship with Britain would hopefully allow them to use the high seas, considering the size of the Norwegian merchant navy by WWII a united Scandinavia could do even better. A neutral Scandinavia with its resources and a massive merchant navy could start to serve as the resource rich region it later became much earlier.
I don't think it could achieve much in colonization though. Too late. There's really no where it could get that would be nice enough allow it to redirect the flow of emigrants from America, so its efforts would be better spent on solving the problems at home that are the direct cause of the emigration.
As for any alt-World Wars. Scandinavia wouldn't be a Great Power, even if it followed a policy of Armed Neutrality, but it would probably be far more likely for Great Powers to try to entice it. Its strategic position and even limited strength could make a difference. An alliance with Germany would weaken any blockade of Germany, and their combined fleets would be better placed to challenge the Royal Navy. An alliance with Britain or Russia would tighten any blockade, and also create an extra front against Germany...Though actually a revanchist Scandinavia biting at the bit against Germany would actually be interesting, since most later Scandinavian Alliance stuff almost always have them adopt the neutrality they generally displayed by this point. A union greatly changing that would be an interesting divergence., if an unlikely one.