With the rise of digital media, protecting image property has become a critical issue. Visible watermarks, once a key tool for copyright protection, have become increasingly vulnerable to removal methods using deep neural networks (DNNs). This poses a significant threat to the ability of visible watermarks to protect image ownership and copyright. To address this increasingly severe challenge, we propose a novel visible watermark protection mechanism based on information hiding. Unlike traditional methods of directly adding perturbations to protected images, we hide adversarial perturbations in watermarked images through a specially designed reversible information exchange (RIE) module, which includes multiple discrete wavelet transform (DWT) and affine coupling blocks. This design can concentrate the perturbations on textured areas of the watermarked images, making them less visually noticeable. Meanwhile, theoretical analysis indicates that the difference between the adversarial image (i.e., the watermarked image after embedding the adversarial perturbation) generated by our method and the watermarked image is completely controllable. To evaluate the proposed mechanism in various scenarios, based on several widely used datasets (i.e., LOGO-Gray, LOGO-H, and LOGO-L), we further synthesize two new datasets, namely LOGO-Multi and LOGO-Full. LOGO-Multi contains images embedded with multiple watermarks, and LOGO-Full contains images embedded with a watermark covering the whole image. Extensive testing on five datasets demonstrates that, compared to the baseline methods, the proposed scheme can greatly improve the visual quality of adversarial images and enhance their capability to resist various watermark removal techniques.