In the case of Singapore, there's nothing particularly unusual to beware of. According to the Crypto Law Survey on Singapore:
The Computer Misuse Act [...] entitles the police [...] to require any person in possession of decryption information to grant access to such decryption information necessary to decrypt data required for the purpose of investigating any such offence. Obstructing the lawful exercise of these powers or failing to comply with an assistance or decryption request is punishable with at most S$10,000 or three years' imprisonment.
But that's for suspected hackers and such, not random visitors, and most countries have similar provisions.
As for the contents of your hard drive, while Singapore does famously ban a whole lot of things ranging from porn to publications by the Jehovah's Witnesses, in this digital age these rules are effectively dead letters and local authorities have admitted as much. On a more practical level, I lived in Singapore for 7+ years, crossing the border in and out several hundred times, and never had Customs express the slightest interest in my laptop, nor have I ever heard of that happening to anybody I knew.
For New Zealand, the same source sums up local laws on cryptography as "None", so there's even less to worry about.