This issue was addressed in United States v. Meng, 2020 BCSC 785.
The authority to extradite is via the extraditing state's treaty with the U.S. and its domestic implementing legislation. In Canada, this is the Extradition Act. Extradition requires consent of the extraditing state and for the requesting state to follow the extraditing state's domestic procedure.
The question you raise is how sanctions of requesting state affect the interpretation of the domestic offence for the purpose of establishing the double criminality requirement.
Critical in this case was that the charged offence was fraud against HSBC (albeit based on alleged concealment of sanctions violations).
See para. 23:
The double criminality question in the committal hearing is therefore whether Ms. Meng’s alleged conduct, had it occurred in Canada, would have amounted to fraud contrary to s. 380(1)(a) of the Criminal Code.
Ms. Meng argued:
that the conduct cannot amount to fraud because in essence the proposed prosecution is to enforce US sanctions laws against Iran, measures that are not part of Canadian law and which, indeed, Canada has expressly rejected.
The Attorney General argued:
that the double criminality analysis may properly take the US sanctions into account as part of the foreign legal backdrop against which the essential conduct is to be understood.
The court agreed with the Attorney General:
The effects of the US sanctions may properly play a role in the double criminality analysis as part of the background or context against which the alleged conduct is examined.