I don't see what he and his attorneys hoped to gain from fighting the extradition. The merit of the case in Sweden is another matter, but that isn't something an extradition court will decide. They don't try the case, they just decide if the request for extradition is a legal one, meets the standards for whatever agreement there is with said nation and so on.
In the case of the UK and Sweden there's a pretty strong extradition treaty so there really wasn't any way there's be another outcome.
Even if he managed to stop it on a technicality of something like the prosecutor not being the right person to be able to request the extradition, Sweden would just go and make a more formal request through their ambassador.
Among countries with strong extradition treaties about the only time it gets denied is if it is a crime they just don't extradite for (minor crimes are often things that they won't) or if the punishment isn't something they'll allow. That has happened with the US and Canada. Canada won't extradite for capital crimes, they aren't ok with the death penalty. So the US has to agree not to seek it, and then the extradition will go ahead.
It really has gotten to the point of rather silly. He's going to have to go and face the charges in Sweden. If they'll stick is a whole different matter, but that is up to the Swedish courts. You don't get to just run to another country and hide from criminal charges, particularly in Europe. What with a bunch of countries near each other and fairly easy borders, they understand the importance of such things.
I'm really not sure what they were going for, other than just a delaying tactic.