Norse pagan faith and christianity co-existed for a couple of hundred years, and it took a long time for christianity to stamp out the old faith - in some senses they never did, as parts of it morphed into folklore and exists to this day. During the 1100-1200s, statues of Frej and Freja were claimed as "local saints", installed in churches and brought out to bless the fields every Spring, to the complaints of local priests, who mostly went unheard as long as the congreation otherwise tithed and followed church law.
That said, if you count by runestones, at least the families wealthy enough to erect them were majority (even if barely) christian long before Blot-Sven were elected King. What complicates matters is that christianity is heavily intermingled with the creation of a unified centralised Kingdom in Sweden - the church benefitted from patronage from the elite, the elite benefitted from central administration, capable monk and priest administrators and above all a literate tradition that eased administration of larger realms.
We don't know for sure, but it is probably that the election of Blot-Sven was more a reaction against encroaching centralisation and curtailing of old rights than it was a religious move.
Denmark and Norway had the advantage of everything being close to the sea - the King's army could be anywhere in the Kingdom in a couple of weeks. That was not the case with Sweden, which is also why Sweden unified much later, and integrated large parts (like Småland, Hälsingland and Medelpad) in the 13th century. IMHO, it is going to be hard to have a Kingdom of Sweden without christianity, because writing letters, wills, instructions and laws are pretty much required to keep the geographically spread out Kingdom together.
You could have the decentralising powers that resulted in Blot-Sven win the power struggle. Most of Sweden will be christian, but the church as an institution will be weak or even non-existing. Other institutions, such as the monastaries, canon law, bishops and probably things like the national ledung will also be absent, and Sweden will remain three different Kingdoms and a bunch of Peasant Republics ruled by their respective thing (Småland, Gotland, Gästrikland, Medelpad and so on).