You'll most likely find you will need to do some level of conversion under the TTMRA. 1st point of contact will be CAA.
None of the operators local to the mountainous area you are thinking about flying into will rent you anything at all until you have done a Mountain Flying course at a minimum. I would recommend you seek advice from the Wakatipu aeroclub. The area around Fox/Franz -apart from being exceptionally mountainous terrain- is also extremely high traffic-density (particularly at the time of year you indicate), all VFR, all doing scenics, all totally reliant on the other guy having some idea of where he is and what he is doing. You'd be far better off doing a scenic with a local operator or hiring an aircraft and instructor to do what you want to.