Within (crystalline silicon) solar cell modeling, a skin means the thin region from the quasi-neutral bulk to the actual surface or metal contact, including e.g. doping profiles, induced band-bending or top-cells of a tandem configuration. A typical highly doped skin is commonly characterized by its main lumped properties: effective recombination via J(0,skin) and lateral conductance via R-sheet. When applied as a boundary condition to bulk carrier transport modeling, it is known as the conductive boundary model. However, the detailed resolution of physics inside the skin is then lacking but required in many cases, and possible complexities, like injection dependence of the lumped parameters, are commonly neglected. This work introduces a general parameterization of skins, which accounts fully for injection dependence and a vertical resistance, and is thus able to accurately describe arbitrarily complex skins by lumped parameters. A "skin solver" is implemented in the solar cell simulation software Quokka3 to solve a detailed skin in 1D and to perform the general parameterization. Additionally, the performance of the multidimensional quasi-neutral bulk (qn-bulk) solver is largely improved compared to Quokka2, enabling, for the first time, the 3D discretization and solution of up to an entire 156 mm x 156 mm solar cell in manageable computing times. Quokka3 can then consistently couple the skin solver with the qn-bulk solver. With this multiscale modeling approach, the user can define and solve a solar cell device including the details of the skins orders of magnitude faster compared to generic device simulation software, without loss of accuracy for the majority of conditions in wafer-based silicon solar cells. The new capabilities are demonstrated by showing how the front phosphorus diffusion of a PERC solar cell can be optimized with unprecedented completeness and accuracy. Besides accurately modeling 3D current transport in the bulk, the single solution domain intrinsically accounts for the busbar influence (both recombination and shading), the distributed resistance of the fingers, and the limited current collection independent of the surface area enlargement by texturing.