Autumnblue
I was at AKL mid October, and they dfinitely had their own pool accessible wheelchair then.
It is a bit like a sun-lounger with wheels. The seat is a fraction lower than a regular wheelchair but side transfer from a regular chair should be no problem. It isn't self propelled, so you will need someone to wheel you in and out of the pool.
The Polynesian also has a zero depth pool and wheelchair, and their wheelchair is a more conventional design. The AKL pool CMs might even borrow the one from the Polynesian if you ask them nicely.
While I was at Polynesian checking out their pool, I asked a CM about 'Pool Hopping' over from resorts without zero depth pools. Although pool hopping is not normally allowed unless you are a DVC member he said that management would almost certainly make an exception for guests with special needs, but I should phone first to double check before coming over.
HugsForEeyore
I am not surprised they would not let you use a regular chair. Setting aside the potential problem of the chair rusting, I suspect a more serious problem would be oil leaking out of the chair's wheel hubs and contaminating the water in the pool.
Andrew