This is a tricky one to explain. In this sentence, mutta would be wrong. I found a long and complex explanation here, but it's in Finnish: http://www.kielitoimistonohjepankki.fi/ohje/483.
Basically, in a sentence like this where you are denying something (Oslo being in Sweden), using mutta would somehow still leave a little bit of "truth" to the claim, whereas vaan just flat out rejects it.
The examples used in the article I linked to (which covers a lot of other kinds of examples, too, but let's just focus on this usage for now) are
Minä en pelkää kuolemaa vaan sairauksia. = I am not afraid of death but rather of illnesses.
Minä en pelkää kuolemaa mutta sairauksia kyllä. (korostus: myönnän pelon; kiistän, että pelon kohde on kuolema') = I am not afraid of death but I am afraid of illnesses. (So there is an admittance of fear, but a rejection of death being the reason for that fear.)
https://uusikielemme.fi/finnish-vocabulary/interesting-words/mutta-and-vaan-the-difference-between-conjunctions/ you can also read the explanation here