If you require truly parametric surfaces, there really isn't any better solution than remodeling from the ground up. I am anticipating that the toy doesn't consist largely of flat surfaces, cylinders, or revolves. (There are a number of solutions that can build these types of parametric surfaces from scans).
Freeform surfaces typically require curves to generate the surface, and there are fewer solutions that can extract the curves from the scan to generate a parametric surface. The curves can be modified later to change the surface. Another way to have a parametric surface is to use subdivision surfaces (via PowerSurfacing plugin below), which are underlying, simplified meshes used to to control the nurbs. The mesh points can be pulled around at will and the nurbs surface will follow, similar to editing curve/spline points.
There are solutions which will create a "dumb" surface or solid in a mostly automatic process, but it is essentially uneditable, although its possible to trim, cut, or put holes in it (adding Features).
If you have SolidWorks Premium or Pro, the Scan to 3D add in might be useful. I don't have it in my license but I have heard from others it has limited use in working with freeform surfaces.
PowerSurfacing RE (SolidWorks plugin) could be really useful, but it depends on what the requirements are downstream. The surface is only editable with the plugin present. So, if you hand off the model, only the features that were created in SolidWorks would be editable, as well as any SolidWorks features added to the PowerSurfacing form, but the PowerSurfacing form by itself would not.
If you also have a Rhino license, Mesh2Surface plugin could be useful and its a lot more affordable than some of the other solutions such as DesignX (or Scan to 3D if you don't have it in your license), but it does not integrate with SolidWorks. Models or curves can be transferred via common formats, but you would loose the parametric nature of the model. The benefit is for a relatively small investment, surfaces or curves could be extracted from scans that could be rebuilt as parametric surfaces.
Thanks for the the detailed response. The example is fictional to illustrate the requirement but the requirement is real. The scans are indeed of complex shapes, and because of the specific nature of the modifications post-scan, working with surfaces rather than parametric 3D objects will become quite tricky from a modeling perspective. It might be that starting from scratch, modeling from the ground up, will be faster and the point cloud data (meshed or not) could be used to verify the fit of the resulting model before it is modified.
Thanks for the suggestions for alternative tools and processes, I’ll look into them.
Thanks Dennis, this is good to know!