I'm not sure what's underlying Key's decision. Maybe it's the case that none of the refugees from there can get to any airport or seaport that could convey them to New Zealand anyway. Maybe NZ has no capacity to sort refugees from ISIS fighters who might wish to come visit.
But if it's just worries about the potential cost of accepting refugees, well, there is perhaps a solution to that. Get a number on the marginal cost to the government of providing assistance to a refugee for the refugee's first couple of years. Set up a PledgeMe drive so those who'd be happy to help support bringing people over can do so. If the cost of an additional refugee is x, and the drive raises 50x, let in 50 more refugees.