… the offender is a committee member who are required to upheld the by-law, not breach it.
You have the option to apply to Fair Trading and NCAT for orders under section 238 (a) removing a person from a strata committee or (c) removing one or more of the officers of an owners corporation from office and from the strata committee.
So how offering a CP-by-law option (slow) is a reasonable option?
When you are challenging someone for not following correct procedure, it helps if you follow procedure yourself. I believe the correct procedure is to invite them to either apply for a CP by-law, stressing that approval is not guaranteed, or remove the air-con.
And is there any statutory obligation for the OC to invite a by-law application?
The OC has a statutory obligation to maintain common property. There is a reasonable expectation that they will do this in the most efficient way available. If you know of a quicker, cleaner, less disruptive and less costly way of doing this, by all means suggest it.
In fact, rather than trying to remove the committee member, I would seek mediation at Fair Trading with a view to taking your committee to NCAT under section 232(2) for failure to fulfil their statutory duties. Either way, the mandatory first step is mediation (which costs nothing) and that is often enough to get things moving but at least is the first step to getting orders at NCAT.
One other thing, reverse cycle air-con is considered a sustainability issue and as such special resolution approval would only require a simple majority at a general meeting.