As long as we're on the tin-foil hat path, being dragged to Sweden would place him into custody there. (I know, he's wanted 'for questioning' - that's what the Red Notice is based on). That would give the USA (which has an extradition treaty with Sweden) plenty of time to build a legal case against him without worrying about him disappearing or pulling more PR stunts.
As long as the USA doesn't charge him with something that is punishable with the death penalty (most EU countries won't extradite suspects that would face that), it's into the bureaucratic legal mill for him.