Doctrine of Speciality
Doctrine of Speciality does not apply only to criminal offences committed in the country the person is being extradited to, according to any source I can find on it. The person can only be prosecuted for crimes named in the extradition request. This includes a prosecution to determine whether or not to extradite to a third jurisdiction. Julian Assange was prosecuted in the United Kingdom and given the opportunity to defend himself against the Swedish extradition request, a criminal justice process that concluded at the UK Supreme Court. Your bold text adds nothing. At any rate, the Swedish prosecution authority have stated publicly that they are bound by this doctrine in this case.
The word "refoulement" either alone or as part of "non-refoulement" appears 15 times in the opinion of the UN Working Group on Arbitrary Detention, for example: "...without any guarantee of non-refoulement to the United States where he faced, in its view, a well-founded risk of political persecution and cruel, inhumane and degrading treatment." Much is made of the UN report, which claims that the UK fail to honour the granting of political asylum by Ecuador. But there is no basis for political asylum because the crime for which he's wanted in Sweden is a sexual offence, not a political one. Assange is currently enjoying diplomatic asylum, which is not recognised. If a requesting nation sought him on the basis of some political crime, then he would be entitled to political asylum. Ironically, the best host in that case would have been Sweden, since it is coded in their extradition treaty with the US to refuse political extraditions. This is why Assange applied for residency there.
Also, why are assurances needed from a democratic country who is a signatory to all the relevant conventions that they will not violate norms of international law? So yes, as they have stated (how the hell do you do a blockquote?):
"Every extradition case is to be judged on its own individual merits. For that reason the Swedish government cannot provide a guarantee in advance that Julian Assange would not be subject to further extradition to the USA."
Quite right. He might be requested for a crime that is judged to be non-political. Sweden can't say before the fact that they will never extradite Julian Assange to the United States under any circumstances. Yet he would enjoy the benefit of two possible vetoes.