It looks like it is all up to the judge. This judge didn't seem to care at all and said even if he is put to death, it will be by injection.
From Edmonton Journal:
Dupre’s lawyers argued against extradition on the grounds he could be sentenced to death if convicted of Sandhu’s murder. But Kiss said judges in extradition hearings cannot concern themselves with the issue of potential punishment, saying extradition committal hearings are a “modest screening device.”
“I note that if he is convicted, the only sentence is death by lethal injection,” Kiss said. “This is simply not a factor I’m permitted to consider at this stage of the extradition proceedings.”