There is no difference in the frame size from your 19-3 (K frame ) and the 586 (L frame). The grips that came on each should be similar with
the only difference being the 19-3 had a small football shaped relief and the 586 had a larger round shaped speed loader relief on the stocks
( assuming they are both 4" or 6" barrel.) So yes, 586 grips would fit a 19 if both were the same, either square butt or round butt.