The rapid proliferation of computing domains relying on Internet of Things (IoT) devices has created a pressing need for efficient and accurate deep-learning (DL) models that can run on low-power devices. However, traditional DL models tend to be too complex and computationally intensive for typical IoT end-nodes. To address this challenge, Neural Architecture Search (NAS) has emerged as a popular design automation technique for co-optimizing the accuracy and complexity of deep neural networks. Nevertheless, existing NAS techniques require many iterations to produce a network that adheres to specific hardware constraints, such as the maximum memory available on the hardware or the maximum latency allowed by the target application. In this work, we propose a novel approach to incorporate multiple constraints into so-called Differentiable NAS optimization methods, which allows the generation, in a single shot, of a model that respects user-defined constraints on both memory and latency in a time comparable to a single standard training. The proposed approach is evaluated on five IoT-relevant benchmarks, including the MLPerf Tiny suite and Tiny ImageNet, demonstrating that, with a single search, it is possible to reduce memory and latency by 87.4% and 54.2%, respectively (as defined by our targets), while ensuring non-inferior accuracy on state-of-the-art hand-tuned deep neural networks for TinyML.