Do you need to use a hand held light meter (i.e. flash meter) for studio photography? If you are dealing with critical light ratios (such as the ratio of the main light to the fill light), then yes, you do. Fashion photographers use hand held meters all the time to assess the light ratio on a model's face and clothes.
However, for much of the work I do in a studio where I can judge the lighting by eye, I don't use a meter at all. I simply look at the exposure and the shadows in the picture as seen in the LCD monitor on the back of the camera, and then I tweak the exposure by adjusting either the power of the flash output and/or the lens aperture. Or, I can vary the distance of the flash to the subject. Then I take another shot and, if necessary, tweak it again until it's exactly what I want.
Remember that shutter speed has no bearing on the exposure (unless the shutter is open for a long time). The exposure for flash is determined by: the light output, the distance of the flash to the subject, and the lens aperture.