What a lovely holiday to look forward to, luckylegs! We did a similar trip to Singapore then NZ in November a few years back, though didn’t cruise but drove around NZ. Yes indeed Singapore was humid but we didn't find it too unmanageable, especially as the air conditioning in public places was so good. Raffles was a real treat to visit, as were the Botanical Gardens.
It was cloudy and also nippy at times in NZ, just looked at my photos and can see I wore a light fleece, a windproof rain jacket and short sleeved tops at various times, So it obviously wasn't cold or wet all the time and there are photos showing very blue skies too.
Relax and enjoy every moment of it, I’d love to do it all again!