Learning a disentangled, interpretable, and structured latent representation in 3D generative models of faces and bodies is still an open problem. The problem is particularly acute when control over identity features is required. In this paper, we propose an intuitive yet effective self-supervised approach to train a 3D shape variational autoencoder (VAE) which encourages a disentangled latent representation of identity features. Curating the mini-batch generation by swapping arbitrary features across different shapes allows to define a loss function leveraging known differences and similarities in the latent representations. Experimental results conducted on 3D meshes show that state-of-the-art methods for latent disentanglement are not able to disentangle identity features of faces and bodies. Our proposed method properly decouples the generation of such features while maintaining good representation and reconstruction capabilities.