I think it would be very hard to get several small Swedish exclaves in Finland, like shown on the map. One major exclave, now, is in my opinion pretty easy. Lets say Sweden keeps Finland until circa 1910, due to skilled alliances, surprising, continued Russian weakness, ASBs, etc. In the meanwhile, Finnish nationalism has diverged a lot from its OTL course, as has Swedish nationalism.
Basically instead of, roughly, "one people speaking two languages" (a gross simplification, of course, but somewhat true IOTL) coming about in Finland, in the Eastern Provinces the people are more clearly divided in two groups that consider themselves either ethnically, culturally, politically and linguistically *Finnish or *Swedish. When and if the *Finnish nation state now breaks off on its own, maybe as a part of a larger disintegration of the Swedish realm, a part of south-west of Finland is, due to diverse butterflies, likely to have a *Swedish majority. Thus, it sticks with Stockholm. Voilá, a Swedish exclave.
This could well happen with both the *Finnish and the *Swedish becoming happy and free in their respective nations. There is also the possibility that this area (centered around Österbotten or, ironically, Egentliga Finland or Finland Proper) might become a Northern Ireland analogue, with *Swedish Unionists and *Finnish Nationalists facing off against each other decade after decade.
If Russia is as strong as IOTL or stronger, it will conquer Finland at some point before 1900, and in that case it will want all of Finland, not leaving to the Swedish ready-made staging areas for an attempt to retake Finland. In that case, exclaves become that much harder to create. One possibility could come about through a different Russian period in Finland post-1809, "now with more Russification!(tm)": the national development of a unified Finland (politically and organisationally as well as in terms of nationalism) is delayed in a major way. This disruption could also happen if Russia takes Finland only around, say, 1850.
If Russia later falls and breaks apart as a result of a Great War or revolution or both, we could have a Finland that also disintegrates internally, part of which asks to rejoin Sweden.
In this scenario, as I guess in the former one too, the absense of a united Finnish state it becomes much easier for Eastern Finland to soon or later fall back under Russian control. Thus, at least for a while, we could have a Swedish exclave/exclaves in a Finland that is part of a Russian state.