Deep joint source-channel coding (DJSCC) has emerged as a robust alternative to traditional separate coding for communications through wireless channels. Existing DJSCC approaches focus primarily on point-to-point wireless communication scenarios, while neglecting end-to-end communication efficiency in hybrid wireless-wired networks such as 5G and 6G communication systems. Considerable redundancy in DJSCC symbols against wireless channels becomes inefficient for long-distance wired transmission. Furthermore, DJSCC symbols must adapt to the varying transmission rate of the wired network to avoid congestion. In this paper, we propose a novel framework designed for efficient wired transmission of DJSCC symbols within hybrid wireless-wired networks, namely Rate-Controllable Wired Adaptor (RCWA). RCWA achieves redundancy-aware coding for DJSCC symbols to improve transmission efficiency, which removes considerable redundancy present in DJSCC symbols for wireless channels and encodes only source-relevant information into bits. Moreover, we leverage the Lagrangian multiplier method to achieve controllable and continuous variable-rate coding, which can encode given features into expected rates, thereby minimizing end-to-end distortion while satisfying given constraints. Extensive experiments on diverse datasets demonstrate the superior RD performance and robustness of RCWA compared to existing baselines, validating its potential for wired resource utilization in hybrid transmission scenarios. Specifically, our method can obtain peak signal-to-noise ratio gain of up to 0.7dB and 4dB compared to neural network-based methods and digital baselines on CIFAR-10 dataset, respectively.