Shutter style does not affect the focus of a pinhole image. The pinhole image, just like a variety of other images, is influenced by a number of factors. On one side, the focal length is important as it determine the degree of sharpness and the extent of the picture that you want to capture. On the other side is the aperture size, which will again determine the degree of exposure and hence, the brightness of the picture.
With pin hole cameras, you also need to make sure that the camera is incredibly still. This ensures that there is no blur. Furthermore, the angle of view is important as well. However, the shutter style doesn’t influence the image in any way.