Alright, so I decided to start and TL arch and need a bit of help on the plausibility, so as I am writing this arch, I will need some feedback.
Here goes:
The riksdag manages to get Gustav in hand and compels him to make peace with France. Sweden then enters into the continental system, closing the Baltic to the British. However by 1812 Russia, Britain, and Sweden sign a secret accord and the continental system is breached.
Napoleon invades Russia, which proceeds like OTL. Sweden remains officially neutral, but is funneling supplies to the Russians in conjunction with Britain. Eventually the Grand Armee is broken at Moscow and the retreat begins. The sixth coalition began its war in Germany and Sweden, whose army never suffered during the Russia invasion and loss of Finland as a recruiting area, contributes a corps nearly double the OTL size. Gustav IV is not present due to the conflicts with the Riksdag. He has not been diposed, but is little more than a figurehead at this point. The Swedish monarchy will never regain its power within the government.
The war proceeds mostly according to OTL, with similar results at Vienna, except that Denmark keeps Norway (butterflies only go so far). However, to compensate Sweden for her involvment in the war, she gets to retain Guadeloupe, which in conjunction with the other Swedish colony of St. Barthelemy, continued to be a nice source of income, as during this period nearly 20% of US exports flowed through their harbors. Additionally the Swedish West Indies Company does not fold in 1813, rather, due to earlier increased illicit trade with Britain during the continental system, it stays in business and an active trading company in East Asia and the Americas.
Europe remains relatively peaceful for a time, as all nations try to reestablish trade and rebuild. Russia is somewhat distracted throughout the '20s and '30s, as border wars to the south and the desire for a warm water port drive imperial ambitions. Additionally the uprisings in Poland focus attention aware from her northern neighbor. The Russians maintain a benign interest in Scandinavia, but come to the conclusion that these minor powers are harmless.
In the meantime, Sweden is involved briefly as a interested power in the Opium wars in China, thanks to their West Indies trading company. This means that they also receive some trading concessions from the Chinese at the conclusion of hostilities. This further involves the Swedes in international trade and shipping. Sweden increasinly modernizes over this period, but also liberalizes, which gives Finns the extra minority rights, thus strengthening the bond between the two peoples. By the 1850's immigration to the US has become a large issue in Sweden, as land reforms do not address the imbalance in land ownership and nearly 1.5 million Swedes and Finns will immigrate in the next 50 years. The greatest policy for maintaining unity between Sweden and Finland, besides the liberalizing economy, education, freedom of press and speech, and taxation reform, is the introduction of universal military service. All 18 year olds are expected to serve 2-3 years in one branch of the military with men from their recruiting districts. This creates helps in the creation of a common identity for the two peoples, despite the rise of nationalism.
Throughout the rest of the 19th century, the Scandinavia powers managed to stay neutral and maintain trade with the rest of Europe despite a series of wars, including the Crimean war and the Franco-Prussian war. Denmark-Norway was not as lucky and was involved in conflicts with Prussia over Schleswig-Holstein, which caused her to cede the territory to the new German state. Despite this territorial loss, Denmark still includes Norway, Iceland, and Greenland, making it, territorially, one of the largest states in Europe. After the creation of the German empire, Denmark, who already had close relation with Sweden, sought even closer economic and political connections. A Scandinavian trade pact would create a de facto free trade zone between the nations that would help industrialization in both nations.
Sweden though maintained cordial relation with the new German state and quickly became a major trading partner. This bond was strengthened by a secret military defensive pact, as Russia increasingly became hostile to the foreign power so close to their capitol. Paranoia in the Tzar's court drove the tension in relations, but as Sweden was a large supplier of raw materials to the German economy, the Kaiser, Frederich III (doesn't experience throat cancer), strongly signaled his support for his northern cousins. It also helped that his son (this Wilhelm does not suffer from a withered arm and is much less...bombastic) was married to the daughter of the Swedish king, Karl Gustav V (all the work of the crafty Bismarck).
By the 1880's the Swedish possessions in the Americas are no longer profitable and France buys them for a decent sum. The Swedish west indies company finally folds, but due to their history of trade in East Asia, other Swedish companies have taken up the business. The turn of the century sees the two Scandinavian powers industrializing rapidly. Swedish inventors were becoming increasing famous for their inventions, dynamite being one of the most widely used of these. The Noble institute would establish the Noble prizes based on the Will of the inventor. His company Bofors, would later go on to become of the largest arms manufacturers in Europe. By the 20th century Sweden would have a population of 7 million and growing. Denmark would have about 4.7 million, but both countries had a rise standard of living that would exceed the population growth.
Scandinavia would have a growing economy that would make it one of the wealthiest areas in the world, but increasing debt would mar the luster of the new prosperity. Large amounts of money were needed from Britain and Germany to finance the growth in industry, specifically Chemical and manufacturing. These debts would eventually be paid down by mid-century, but the experience structured national perceptions to focus on personal savings. This would help create the banking boom that would serve to unseat London and the finance capitol of the world (this was also helped by the fall of British economic dominance and the rise of German).
After the last major conflicts on the continent the resulted in modern Germany, peace had been the rule outside of the Balkans. Despite several wars involving southern European powers with the Ottomans, the 20th century in Europe was possibly the most peaceful in the history of the continent. Eventually, Ottoman resurgence, driven by oil revenues and a modernized government, settled the Balkans and stopped the slow bleeding of land that had plagued the middle eastern giant.
Eventually though, economics and the growth of peripheral powers created tensions within Europe that threated to bring the great powers to the brink of war. The fall of British power had left a bitter nation envious of the new giants. The increase calls for Indian independence had sapped much of the power of the Empire, as British units were required in increasing numbers to combat the rise number of riots and insurgency that followed these calls. France had seemed to accept its status as a second tier power in the European pecking order, but still was resolute to assert itself. But she too was caught up in colonial disturbances by the fifties. Germany had become the largest economy in Europe and had one of the most advanced in the world. Scandinavia was the banking giant and a large industrial power itself. This region also was able to boast about 22 million people by the 1950's. Russia was the one power that had unrealized potential. The bear had been plagued by unrest and violence, which resulted in either repression and more violence, or an uneasy liberalizing period that slowly gave the Duma more power. Eventually, a situation similar to Germany's in the 1910's had emerged. The government was still controlled by the Tzar, but required parliamentary approval for most actions. The economy had grown enormously, but remained in Germany's and America's shadows. Russia was in many ways a resource supplier to Europe, but also, increasingly a manufacturing giant (like OTL China). They also had an increasingly large military and a desire 'for their place in the sun'. Tensions mounted over Russia's desire for THE great power status, which left Europe on wars edge by mid century.