You need to cert when:
"Wheel and tyre changes (non-OEM items), e.g. wheels wider than the bodywork, or with spacers or a different offset to the OEM design. Tyres with more than 5% greater rolling circumference than the OEM tyres."
http://www.lvvta.org.nz/index.html
The fact that you have a cert for other items shouldnt impact on other legal changes that dont require a cert.
Obviously you cant put lower profile tyre / wheel combos that would impact on the existing cert causing the car to be lower to the ground. The measurement however is from the wheel center to the guard (which shouldnt change)