We consider a class of nonlinear time-varying switched control systems for which stabilizing feedbacks are available. We study the effect of the presence of a delay in the input of switched nonlinear systems with an external disturbance. By contrast with most of the contributions available in the literature, we do not assume that all the subsystems of the switched system we consider are stable when the delay is present. Through a Lyapunov approach, we derive sufficient conditions in terms of size of the delay ensuring the global exponential stability of the switched system. Moreover, under appropriate conditions, the input-to-state stability of the system with respect to an external disturbance is established.