This is not a strictly legal answer, but your SM works for the OC, not the other way round. The OC made its wishes known when it voted for the new by-law. So stand your ground. The recalcitrant owner can take you to NCAT and argue that he/she wants to install aircon under an outdated by-law with no documentation. Good luck to him or her.
BTW I recently assisted an owner who objected strongly to providing documentation for a renovation. Turned out that the owner simply didn’t understand what was required so I made a list and ticked off each document as it was provided. Once the owner saw this structure and had a list to work through, the documents started to appear. Owner also didn’t know how to look up trades’ licenses so I did that for her. Took a bit of time, but we got there in the end. I actually felt sorry for her once I realised that her aggression and refusal to comply stemmed from feeling out of her depth and not up to the task.