There are two different kinds of shadows that you will care about with portraiture. One kind of shadow is shadows of facial features on the face itself. These shadows are often consdiered desirable, as they give shape and dimentionality to an otherwise 2D picture.
Typically there will be one major light source that is away from the camera and pointed towards the subject. The further away from the camera the camera, the longer the shadows will appear. Typical placement is at about a 45 degree angle away from the camera. If the light is on the same axis as the camera, located on or very close to the camera, therre will be few or no shadows on the subject.
Another way that the quality of shadows is controlled is by the use of lighting modifiers such as umbrellas to increase the apparent size of the light source with respect to the subject. A small light source like a bare speedlight will create shadows with very sharp edges. A large light source like a flash shoot through an umbrella placed close to the subject will create shadows with very indistinct, diffuse borders.
If an off axis main flash is used a second flash placed near the camera, with a lower power setting than the main flash, will make the shadows less dark. Alternative, a large white card can be used to reflect the main flash into the shadows to make them less dark.
A second kind of shadow that may appear in portraits is the shadow of the subject onto the background. This is typically considered undesirable and is controlled or eliminated in a number of ways. One way is to increase the distance between the subject and the background, so that any shadow falls in a place that isn't seen by the camera. Using a large light source like an flash with umbrella will make any shadows on the background less distinct and thus less objectionable. Finally, a light source may be pointed at the background to illuminate it, and if the light source is bright enough, it will eliminate any shadows.
So to achieve a completely shadowless portrait given the equipment in the original question, the best option would probably be to set up the speedlight using one of the white umbrellas (either bounce or flash through) immediately behind and slightly above the camera.