It seems to me that furniture-quality wood products are OK. At least that's the impression I got when I cruised through the MAF "banned items" list. They might even allow kiln-dried lumber.
You could start here for some bedtime reading:
Ministry of Agriculture & Forestry, New Zealand
Just traipsing through that site, I found this quote, which was about plant products which were even more suspect than cedar:
"Please note these items are NOT necessarily prohibited, they require inspection. In many instances a declaration as to the state of manufacture may lift this requirement. Our inspections are generally to determine cleanliness and the presence or otherwise of insects or prohibited items" (source page:
Personal Effects). It sounds like you need to declare wood products.