To formalize a Power of Attorney with the Spanish Consular authorities in New Zealand, you will have to come to Wellington in person.
Honorary Consular Offices do not have this ability. Such acts can only take place at the Consular Posts, as you must sign it in the presence of the Consul.
There is, however, an alternative route. You could go before a notary public of New Zealand and sign the Power of Attorney. Then you must send that POA to the Department of Internal Affairs of New Zealand (Department of Internal Affairs http://www.dia.govt.nz/
If in the end you decide to grant the power here with us, you must send: a) a scanned copy of the draft of the POA (you should get this draft from your lawyer in Spain), this scanned copy must be in WORD DOCUMENT. b) a scanned copy of your passport or ID card c) a scanned copy of passport or ID of the person you want to grant power.
With all this, you would be given an appointment, according to the availability of the Consul to appear and sign. At the time of appearance, you must bring your identity card or passport and pay the appropriate fee (the fee will vary according to the length of the document).