Semi-transparent volumetric cloud = your image data, so you already have it. No processing is performed on the data, it is visualized directly using raycasting. Volume rendering visualization parameters are mostly defined by transfer functions (opacity, color, gradient), which are saved in the Slicer scene.
STL file cannot store volumetric cloud, it only stores a surface mesh = hard boundary of your printed object.
What confuses most people that volume rendering may give the illusion that there is a distinct surface computed from the data, but actually what you see is a volumetric cloud.