Blown highlights are an exposure issue. If you are blowing out your highlights, then your exposure is too high (too much)....so reduce your exposure (shutter speed, aperture & ISO). With lighter skin tones, this is less of an issue, not because there is less direct reflection, but because there is more diffuse reflection, so the highlights don't stand out as much. With darker skin tones, there is less diffuse reflection, so the shiny highlights stand out more. One way to deal with this, is to fill more of the 'family of angles' by using a very soft light source (large and close to the subject).
Shininess is a property of direct reflection, which we all have in our skin, to one degree or another. It's the direct reflection of the light source...so if you can move your lights (or position your subject) so that the angle of the light doesn't match the angle of the camera (bouncing off the subject) then you may be able to eliminate the shiny reflection. This has to do with understanding the family of angles. Of course, with a round subject, it will be hard or impossible to get rid of it completely. And of course, the size, shape and position of the highlight will be a result of your light source. So if you can make your light source very soft (large and close to the subject) then the highlight will be more spread out...and if you set your exposure so that it's not blown out, it probably won't look too bad.
And of course, you can try to get rid of pesky highlights in Photoshop. The healing brush and the clone stamp are usually a good place to start.