A low-cost oil bath synthetic route is presented to produce uniform and highly crystalline layered cobalt hydroxide nanocones (NCs) intercalated with dodecyl sulfate anions (C12H25OSO3-, DS-). A new exfoliating procedure, by gradually unravelling/unzipping these NCs through heat treatment in formamide-water binary solution, is developed to prepare unilamellar nanosheets. Moreover, the NCs can be readily modified with various inorganic or organic anions via a conventional anion-exchange process at ambient temperature. The exchanged product, for example, NO3--intercalated NCs, can be more easily and rapidly transformed into cobalt oxides (e.g., Co3O4 and CoO) than the original DS--intercalated form while retaining a conical feature. Both the cobalt hydroxide NCs and exfoliated nanosheets are electrochemically redoxable, exhibiting a Faradaic pseudocapacitive behavior. The magnetic measurements further reveal both antiferromagnetic behaviors for transformed Co3O4 and CoO NCs. Their Neel temperature values are lower than those of bulk oxides due to finite size and geometric confinement effect. The peculiar conical feature of NCs with a hollow interior and tunable layer spacing, as well as exfoliated unilamellar nanosheets with all surface area exposed, may show promise for potential applications in electrochemical energy storage and magnetic devices.