Cavitation is a function of pressure drop, downstream pressure, vapor pressure and valve pressure recovery factor.
The valve pressure recovery factor is highest for wide open ball valve (Fl, Kc is lowest) so closing the valve more will not cause cavitation in itself.
What causes the cavitation is the system hydraulics; when you close the valve the downstream pressure falls and cavitation occurs.
You just need to calculate the downstream pressure at different valve openings (different Cv's) and using the pressure recovery factor for these openings, calculate the onset of cavitation.  You can use Fisher First or other commercial control valve software from Masoneilan, Valtek etc.
By the way, most partial stroke tests to verify operability (for safety system testing) for clean fluids use 10% as the stroke which normally would not cause any problems with upsetting the process flow).

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