Typically lower layer heights help with threads. Also, if you have a small cross section/layer, it might help to print two or three screws simultaneously to allow each layer to cool off before the next one is layered on top. Threads print best if they are printed with the axis of the screw shaft aligned with z. The smaller nozzle will help resolve smaller features, but if you aren’t printing features that are smaller than, say, 1mm in x and y then you probably won’t see much of a difference between a .35mm and, say, a .15mm nozzle
If you post the .stl or a link to it you might just get a good .ini and .gcode in return!