A variety of pruning methods have been introduced for over-parameterized Recurrent Neural Networks to improve efficiency in terms of power consumption and storage utilization. These advances motivate a new paradigm, termed `hyperpruning', which seeks to identify the most suitable pruning strategy for a given network architecture and application. Unlike conventional hyperparameter search, where the optimal configuration's accuracy remains uncertain, in the context of network pruning, the accuracy of the dense model sets the target for the accuracy of the pruned one. The goal, therefore, is to discover pruned variants that match or even surpass this established accuracy. However, exhaustive search over pruning configurations is computationally expensive and lacks early performance guarantees. To address this challenge, we propose a novel Lyapunov Spectrum (LS)-based distance metric that enables early comparison between pruned and dense networks, allowing accurate prediction of post-training performance. By integrating this LS-based distance with standard hyperparameter optimization algorithms, we introduce an efficient hyperpruning framework, termed LS-based Hyperpruning (LSH). LSH reduces search time by an order of magnitude compared to conventional approaches relying on full training. Experiments on stacked LSTM and RHN architectures using the Penn Treebank dataset, and on AWD-LSTM-MoS using WikiText-2, demonstrate that under fixed training budgets and target pruning ratios, LSH consistently identifies superior pruned models. Remarkably, these pruned variants not only outperform those selected by loss-based baseline but also exceed the performance of their dense counterpart.