Neural networks (NNs) are capable of learning complex patterns and relationships in data to make predictions with high accuracy, making them useful for various tasks. However, NNs are both computation-intensive and memory-intensive methods, making them challenging for edge applications. To accelerate the most common operations (matrix-vector multiplication) in NNs, hardware accelerator architectures such as computation-in-memory (CiM) with non-volatile memristive crossbars are utilized. Although they offer benefits such as power efficiency, parallelism, and nonvolatility, they suffer from various faults and variations, both during manufacturing and lifetime operations. This can lead to faulty computations and, in turn, degradation of post-mapping inference accuracy, which is unacceptable for many applications, including safety-critical applications. Therefore, proper testing of NN hardware accelerators is required. In this paper, we propose a \emph{one-shot} testing approach that can test NNs accelerated on memristive crossbars with only one test vector, making it very suitable for online testing applications. Our approach can consistently achieve $100\%$ fault coverage across several large topologies with up to $201$ layers and challenging tasks like semantic segmentation. Nevertheless, compared to existing methods, the fault coverage is improved by up to $24\%$, the memory overhead is only $0.0123$ MB, a reduction of up to $19980\times$ and the number of test vectors is reduced by $10000\times$.