In this paper, we present a degradation-aware privacy control strategy for smart meters by taking into account the capacity fade and energy loss of the battery, which has not been included previously. The energy management strategy is designed by minimizing the weighted sum of both privacy loss and total energy storage losses, where the weightage is set using a trade-off parameter. The privacy loss is measured in terms of Bayesian risk of an unauthorized hypothesis test. By making first-order Markov assumptions, the stochastic parameters of energy loss and capacity fade of the energy storage system are modelled using degradation maps. Using household power consumption data from the ECO dataset, the proposed control strategy is numerically evaluated for different trade-off parameters. Results show that, by including the degradation losses in the design of the privacy-enhancing control strategy, significant improvement in battery life can be achieved, in general, at the expense of some privacy loss.