Dog door installed in westmere, auckland

Dog door required through exterior wall that has weatherboard cladding on the outside. We a Dog Mate medium size door installed in our place in Wellington, and keen to do the same https://www.catdoorcompany.co.nz/product/dog-mate-medium-dog-door/ The cat door company said that the wall is too thick for the medium door and want us to install the small door, so would be good to check if that is actually a thing. Cheers Due date : Before Wed, 24th Dec Location: Westmere, Auckland Thanks