I'm not an expert on the NZ military either, although I am a Kiwi so I know where to look for info. From recent historical evidence, a large deployment out of NZ is unlikely. We simply don't have the capabilities to support a large operation out-of-country; we generally piggy-back off of others.
The way I see it, the first Asian front to kick off (say, Korea) would get some NZers, especially if Aus sent troops. First in would be the SAS, and probably a medical detachment, and some Hercs doing support work. If there was a larger need, regular troops would come a bit later (would likely need training and reserve call-up).
Then if Indonesia went off, much of that might get called home, or to Australia, to support from there. The Navy would lend some support, likely a frigate joining the Aussies. And we still had a combat airforce then, so No. 2 Squadron (upgraded Skyhawks) would probably be helping too (No. 2 was equipped with ex-Royal Aus. Navy A4s, and based in NSW, Aus. in the 90's).
All up, I would say a squadron of SAS, a battalion of regulars (after training), some support troops, a few Hercs, a frigate and No. 2 Squadron would all that would end up outside of NZ.
Oh, and we kinda got booted out of ANZUS over that whole "no nukes" thing
Wonder if Marsden Point oil refinery received some attention nevertheless.....
Andrew