While the south and the west of Finland had a lot of Swedish-speakers, we have to remember that in the Finnish interior and in the east native Swedish speakers were ever only a thin veneer (or a capstone, if you may) above a mainly Finnish-speaking populace. Because of this, I believe Finnish would still be the majority language among the ordinary people east of the Gulf of Bothnia by the mid-19th century when we could expect a *Fennoman movement to grow and something like Finnish nationalism become a significant movement. The seeds for this had been planted in the 18th century already, among the Turku/Åbo intelligentsia above all. Due to a rising nationalist thought, any overt efforts at linguistic and cultural Swedification of the main part of the Finnish provinces in the latter part of the 19th century would certainly meet opposition. We will certainly see a lot of interest into the Finnish language, and efforts at codification and so on - a national-romantic effort to make Finnish into a "language of culture", of learning and literature, instead of just a "lowly peasant tongue" many in Sweden proper saw it at the time.
So unless Sweden takes very draconian measures to put down the Finnish language and culture (and such a course of action might drive the Finns into seeking Russian help against Stockholm), I don't think we will see the Finnish language go the way of Gaelic by, say, the mid-20th century - there were always comparatively more Finnish-speakers in the Swedish realm than there were Gaelic-speaking Irish people in the British one, after all. The high proportion of Finnish-speakers in the Swedish realm (in the 19th century, 20-30%) and the need to maintain some loyalty and stability among them (against the Russian interests) would be too significant for this.
At worst, for Finnish language and culture that is, I'd suggest native Swedish speakers might just become a small majority in the Finnish provinces by 1950 or so - and even that might require a lot of Swedish migration into Finland, and perhaps losing some of the eastern parts of the Finnish areas to Russia, making some of the Finnish-speakers in the East Russian subjects instead.
Come to think of it, that might be the nightmare scenario for the Finnish language and nation in the 19th century - the Finnish areas being divided to two parts by the Russians and the Swedish, and never being able to form a one single, politically and administratively cohesive unit like the Finnish Grand Duchy IOTL. But if all of current Finland stays with Sweden, or even something like Finland with the OTL Grand Duchy borders, we would likely see the formation of a Finnish nation within the Kingdom of Sweden, perhaps eventually as a (more or less) autonomous unit - whether it would ever gain independence is another matter.