Amphiphilic copolymers of alkyne functionalized 2-hydroxyethyl methacrylate (AlHEMA) and poly(ethylene glycol) methyl ether methacrylate (MPEGMA) with graft or V-shaped graft topologies were synthesized. The functionalization of poly(ε-caprolactone) (PCL) with azide group enabled attachment to P(AlHEMA-co-MPEGMA) copolymers via a “click” alkyne-azide reaction. The introduction of PCL as a second side chain type in addition to PEG resulted in heterografted copolymers with modified properties such as biodegradability. “Click” reactions were carried out with efficiencies between 17–70% or 32–50% (for lower molecular weight PCL, 4000 g/mol, or higher molecular weight PCL, 9000 g/mol, respectively) depending on the PEG grafting density. The graft copolymers were self-assembled into micellar superstructures with the ability to encapsulate active substances, such as vitamin C (VitC), arbutin (ARB) or 4-n-butylresorcinol (4nBRE). Drug loading contents (DLC) were obtained in the range of 5–55% (VitC), 39–91% (ARB) and 42–98% (4nBRE). In vitro studies carried out in a phosphate buffer saline (PBS) solution (at pH 7.4 or 5.5) gave the maximum release levels of active substances after 10–240 min depending on the polymer system. Permeation tests in Franz chambers indicated that the bioactive substances after release by micellar systems penetrated through the artificial skin membrane in small amounts, and a majority of the bioactive substances remained inside the membrane, which is satisfactory for most cosmetic applications.