NZCAA do not distinguish between paying passengers (charter) and paying passengers (RPT). But they do discriminate on number of pax seats & max cargo capacity. Hence parts 135, 125 and 121 respectively.
A mandatory sim check sounds like Part 121 to me. There is certainly no CAA restriction on a private operation into any NZ airfield. Airfield operators are of course free to specify any requirements they like, such as PPR.