Cross-speaker style transfer aims to extract the speech style of the given reference speech, which can be reproduced in the timbre of arbitrary target speakers. Existing methods on this topic have explored utilizing utterance-level style labels to perform style transfer via either global or local scale style representations. However, audiobook datasets are typically characterized by both the local prosody and global genre, and are rarely accompanied by utterance-level style labels. Thus, properly transferring the reading style across different speakers remains a challenging task. This paper aims to introduce a chunk-wise multi-scale cross-speaker style model to capture both the global genre and the local prosody in audiobook speeches. Moreover, by disentangling speaker timbre and style with the proposed switchable adversarial classifiers, the extracted reading style is made adaptable to the timbre of different speakers. Experiment results confirm that the model manages to transfer a given reading style to new target speakers. With the support of local prosody and global genre type predictor, the potentiality of the proposed method in multi-speaker audiobook generation is further revealed.