You might be misreading the extradition criterion
The UK–USA extradition treaty has an example of the clause you're asking about:
- An offense shall be an extraditable offense if the conduct on which the offense is based is punishable under the laws in both States by deprivation of liberty for a period of one year or more or by a more severe penalty.
Similar wording is used in all other treaties that I have reviewed:
- UK–Algeria ("offences which
are punishable under the laws of both Parties by imprisonment or other deprivation of liberty for at least a period of one year")
- UK–Argentina (no extradition when "the maximum punishment for the offence is imprisonment for less than one year")
- UK–Bolivia (same as Argentina)
- UK–Chile (same as Argentina)
- UK–U.A.E. ("offence is based is punishable under the laws of both Parties by deprivation of liberty for a period of at least one year")
If there is a treaty that requires there to be a mandatory minimum punishment of at least one year, I have not found it. While you say that "[u]sually, the minimum sentence for a crime has to be 12 months for an extradition to be allowed" and "[e]xtraditions are based on minimum sentence in the UK," my review of the treaties makes me doubt that. The rest of this answer explains how to interpret the clauses quoted above.
It is enough that the offence gives rise to the "possibility of a term of imprisonment or other form of detention of more than one year."
The inquiry is focused on the offence that the conduct is alleged to give rise to and the range of punishment available for that offence generally. E.g. an offence with a minimum punishment of a fine and a maximum punishment of 16 years in prison is an offence that is "punishable... by deprivation of liberty for a period of one year or more."
Said another way: it is not necessary that the offence have a mandatory minimum of one year imprisonment. It is enough that the offence gives rise to the "possibility of a term of imprisonment or other form of detention of more than one year." See Canada v. Barrientos, 1995 ABCA 468 (CanLII) at para 103, Hetherington J., dissenting; but appeal allowed, for the reasons of Hetherington J. by the SCC in Canada v. Barrientos,  1 S.C.R. 531. In Barrientos, the courts were interpretating Article 2 of the Canada–U.S. extradition treaty, with wording substantially similar to the UK extradition treaties I reviewed above: "provided these offenses are punishable by the laws of both Contracting Parties by a term of imprisonment exceeding one year."
One remaining question is whether the decision-maker needs to consider the specific facts of defendant's conduct and make a preliminary estimation as to whether in fact a term of imprisonment more than one year is likely. This position has not been adopted in Canada. At the stage where a judge or Minister of Justice is determining the authority to proceed, this is not to become a "sort of sentencing hearing." See USA v. English, 2002 BCSC 1902 at para 23.