At this point, its not clear that Sweden will still want him. There's just a single charge and if put on trial, memories would have faded so Sweden may take a pass.
This doesn't stop the UK for enforcing the jumping bail. And they will do that since he's cost them a pretty penny in terms of overtime.
He 'walks out' or is dumped out, he will face UK music, then back to Australia. Then its up to Jeff Sessions to see if the US wants him or not.