Hi. My understanding is that yes, all non-essential businesses that are able to operate in a contactless way (i.e. online) and observe safe workplace practices (i.e. working from home, safe distancing etc) will be able to courier items with NZ Post.
My company Parcelport.co.nz, is an online courier platform. We partner with the major courier and freight companies (including NZ Post). Its free to use our service so please don’t hesitate to look us up. More than happy to help. Jeff