Am I required to pay Zakat on my money held in a bank account outside my place of residence before going for Hajj, or can I perform Hajj first and then pay Zakat later?

Zakat is immediately obligatory, and it is not permissible to delay it except for a benefit or a need. Therefore, one should hasten to disburse it. If that is not possible, then there is no harm in delaying it until after Hajj, with the obligation of writing that down in the will; because it pertains to the rights of the poor, in preservation of these rights and to clear one's conscience.