In this paper, we address automating and systematizing the process of finding black-box models for virtual analogue audio effects with an optimal balance between error and latency. We introduce a multi-objective optimization approach based on hardware-aware neural architecture search which allows specifying the optimization balance of model error and latency according to the requirements of the application. By using a regularized evolutionary algorithm, it is able to navigate through a huge search space systematically. Additionally, we propose a search space for modelling non-linear dynamic audio effects consisting of over 41 trillion different WaveNet-style architectures. We evaluate its performance and usefulness by yielding highly effective architectures, either up to 18× faster or with a test loss of up to 56% less than the best performing models of the related work, while still showing a favourable trade-off. We can conclude that hardware-aware neural architecture search is a valuable tool that can help researchers and engineers developing virtual analogue models by automating the architecture design and saving time by avoiding manual search and evaluation through trial-and-error.