See https://www.aucklandmuseum.com/war-memorial/online-cenotaph/record/C28746
killed on active service. So according to that record he was not killed by his fellow New Zealanders. While 5 New Zealanders were shot for desertion in ww1, I can find no evidence for any executed in WW2
see https://en.wikipedia.org/wiki/Desertion \
even the USA only executed 1 soldier for desertion in WW2
If he was executed for desertion (It would not have been for just being a conscientious objector) he would not have been buried with any honour, He would have been probably been buried in an unmarked grave.
Ok, I have re-read the comments on the Cenotaph site. Thanks, Will. He may well have been a conscientious objector, but was sent to serve anyway and was killed on active service. I have to be more careful!!