Hi, If you don't feel anyone in your family would serve as the executor of your estate or you just felt it would be best dealt with by the public trustee then its probably a good option.
Section 52 of the Public Trustee Act 1995 states that the public trustee can hold your will for safe custody. So I think that would answer both questions, they wouldn't need find and no body would have access to tamper with the document.
PUBLIC TRUSTEE ACT 1995 - SECT 52