I think that push button you mention was discontinued to the cheaper screw that he asked about.
Accurate, yes, we had two of them some 30yrs ago, and along with the other HS semi autos I had, were surprisingly accurate for what was a kit gun. I recognized the potential of that plastic grip/mag frame aging and getting brittle, so I sold them before it happened to me. I still see them around from time to time, still shooting good. As said, dont drop it and you will be OK.