My understanding is that your PCOS won't go away just because you get a hysterectomy.
Your insulin resistance isn't caused by your ovaries, but rather by your pancreas not working efficiently (which is also caused by being overweight,

because our bodies are too large for the pancreas to work right).
Women make some testosterone in their ovaries, but testosterone is also made by the adrenal glands. A lot of doctors think that part of the PCOS symptoms is a misfiring of the adrenal glands, not just the ovaries (they think the ovaries are a secondary symptom of a large issue elsewhere).