Hi John,
HMNZS COOK was an RNZN depot at Clyde Quay, Wellington, and training establishment at Shelly Bay, Wellington, NZ. Commissioned 01.01.1943 and paid off 18.06.46.
Although there is nothing to support this, my assumption is that your father was transferred to the accounts of HMNZS COOK while awaiting his discharge in New Zealand. They would be responsible for his pay account and matters relating to naval discipline but he would have had no duties relating to the establishment. Likewise for HMNZS Philomel, also an RNZN depot at Devonport, Auckland.