Can the US President give a guarantee that the Supreme Court will decide a case in a certain manner? Because that's what that means.
Sweden is a country with laws, and an independent judiciary. Sweden has extradition treaty with the US (as do many people). If the USA follows a procedure, then the Swedish courts must hand someone over (and vice versa). That's what the (Swedish) law says. You're asking the Swedish government to guarantee that the Swedish courts won't decide a particular case in a particular manner.