It was only the rape charge has was scared of. He was never really scared of extradition to the US, for if he had been, he would scarcely have come to the UK, the US's closest ally, a country with a much more watertight extradition deal with the US than Sweden has.
The risks of extradition from the UK to US were always at least as high, and by any reasonable standard much higher, than those from Sweden.
Sweden's extradition treaty to the US specifically excludes political offences, which means spying. Even now Sweden is refusing to extradite to the US a US citizen accused of spying on Americans on behalf of Cuba.