Your challenge, should you choose to accept it, is to give Finland (either Swedish or Russian) independence-of-sorts under a Bonaparte. Have at it!
According to Wikipedia: "His wish to marry Tsar Paul I of Russia's daughter, Grand Duchess Anna, caused alarm in Austria, who were afraid of being sandwiched between two great powers allied with each other. At the persuasion of Count Metternich, a marriage between Napoleon and Marie Louise was suggested by Emperor Francis to the Count of Narbonne but no official overture was made by the Austrians. Though officials in Paris and Austria were beginning to accept the possibility of the union, Marie Louise was kept uninformed of developments.
Frustrated by the Russians delaying the marriage negotiations, Napoleon rescinded his proposal in late January 1810 and began negotiations to marry Marie Louise with the Austrian ambassador, the Prince of Schwarzenberg. Schwarzenberg signed the marriage contract on 7 February. Marie Louise was informed of the marriage by Metternich."
If I recall correctly, Napoleon ended up marrying Marie Louise of Austria because Josephine did not give him an heir and he wanted to further his alliance with Austria. I may be mistaken but I do not believe that there were any Russian princesses available for Napoleon.
This is an interesting challenge and I will have to look more into the possibilities.
EDIT: According to Wikipedia: "His wish to marry Tsar Paul I of Russia's daughter, Grand Duchess Anna, caused alarm in Austria, who were afraid of being sandwiched between two great powers allied with each other. At the persuasion of Count Metternich, a marriage between Napoleon and Marie Louise was suggested by Emperor Francis to the Count of Narbonne but no official overture was made by the Austrians. Though officials in Paris and Austria were beginning to accept the possibility of the union, Marie Louise was kept uninformed of developments.
Frustrated by the Russians delaying the marriage negotiations, Napoleon rescinded his proposal in late January 1810 and began negotiations to marry Marie Louise with the Austrian ambassador, the Prince of Schwarzenberg. Schwarzenberg signed the marriage contract on 7 February. Marie Louise was informed of the marriage by Metternich."
If Ekaterina is still free will really Alexander decide to risk or fight a war only for not marrying Ekaterina to Napoleon? I do not think who his mother's influence will be enough for that or also Alexander's own opinion of Napoleon if was unfavorable... Better sacrificing his sister to an unappy marriage to a very powerful parveneu than broke an useful alliance and fight a war...The problem with that though would be the considerable influence the Dowager Empress Maria Feodorovna had on Alexander. If she were somehow removed from the equation then the marriage between the two may be easier to pull off.
Because OTL Alexander hastly married off Ekaterina before Napoleon was free to ask her hand and Anna was really too young for the marriage and Napoleon needed to marry and have a son as soon was possible and Alexander instead of refusing his sister's hand to Napoleon played on her age. If Napoleon ask the hand of Ekaterina, Alexander's choices will be of said yes or no. If he refuse his sister's hand to his ally he will almost surely broke that alliance and likely obtain a declaration of war for having insulted Napoleon and his honor (and Alexander will not be able do deny that)Why would the refusal of marriage result in a war with Napoleon? It didn't OTL which resulted in Napoleon going to the Austrians. The resulting war was caused by Napoleon's actions over a few years.
If there is accuracy in the sources that I have read then Alexander, while on decent terms with Napoleon, was still cautious. He was also described as an enigma by contemporaries and a "shifty Byzantine" by none other than Napoleon. While his mother's influence may not be enough there is still the factor of his personality. Personality isn't something that is immediate. To put it simply, personality is developed over time and if there is to be a different Alexander in regard to personality then you need to go back to his childhood. However, with a POD like that one can only imagine the butterflies...