This paper focuses on top-k query in cluster-based multi-hop wireless sensor networks (WSNs) employing wake-up receivers. We aim to design wake-up control that enables a sink to collect top-k data set, i.e., k highest readings of sensor nodes within a network, efficiently in terms of energy consumption and delay. Considering a tree-based clustered WSN, we propose a cluster-based wake-up control, which conducts activations and data collections of different clusters sequentially while the results of data collections at a cluster, i.e., the information on provisional top-k data set, are exploited for reducing unnecessary data transmissions at the other clusters. As a wake-up control employed in each cluster, we consider two different types of control: countdown content-based wake-up (CDCoWu) and identity-based wake-up (IDWu). CDCoWu selectively activates sensor nodes storing data belonging to top-k dataset while IDWu individually wakes up all sensor nodes within a cluster. Based on the observation that the best control depends on the number of cluster members, we introduce a hybrid mechanism of wake-up control, where a wake-up control employed at each cluster is selected between CDCoWu and IDWu based on its number of cluster members. Our simulation results show that the proposed hybrid wake-up control achieves smaller energy consumption and data collection delay than the control solely employing conventional CDCoWu or IDWu.