Our paper deals with a new computational approach to optimal control design for a class of switched systems. The control strategy we propose is based on the conventional proximal point method applied to a specific optimal control problem (OCP) with switched dynamics. The class of OCPs under consideration is widely applicable in optimization of real-world electronic systems. We create constructive approximations for the initially given sophisticated OCP, establish numerical stability (consistency) of the resulting algorithm, and develop an optimal control strategy. We finally discuss some implementability issues, study an illustrative example, and also point to possible generalizations of the elaborated control design in the context of nonlinear hybrid systems.