The hypervapotron (HV) has been demonstrated to be a superior thermal management (TM) and high heat flux removal (HHFR) technique for fusion reactor plasma-facing component applications involving a single-side absorbed heat flux (up to between 20 and 30 MW/m2). However, the conjugate heat transfer HV flow channel (HFC) only can be optimized completely when the related HHFR controlling parameters have been identified. In an earlier work, Part I of the present effort, we identified three high heat flux-side controlling TM and HHFR dimensionless parameters and a characteristic temperature difference. In the present work, six HV wall conjugate heat transfer dimensionless primary controlling parameters and five secondary controlling parameters have been identified. The controlling parameters include the effects of (1) most geometric specifications of the array of fins; (2) variations in the HV wall thermal conductivity and heat transfer coefficient; (3) effective Biot numbers characterizing effects that include the fin array, a typical fin example, and the side walls; (4) the HFC unobstructive portion flow aspect ratio, and (5) the HFC wall aspect ratio.