Synthesis-based steganography without embedding (SWE) methods transform secret messages to container images synthesised by generative networks, which eliminates distortions of container images and thus can fundamentally resist typical steganalysis tools. However, existing methods suffer from weak message recovery robustness, synthesis fidelity, and the risk of message leakage. To address these problems, we propose a novel robust steganography without embedding method in this paper. In particular, we design a secure weight modulation-based generator by introducing secure factors to hide secret messages in synthesised container images. In this manner, the synthesised results are modulated by secure factors and thus the secret messages are inaccessible when using fake factors, thus reducing the risk of message leakage. Furthermore, we design a difference predictor via the reconstruction of tampered container images together with an adversarial training strategy to iteratively update the estimation of hidden messages. This ensures robustness of recovering hidden messages, while degradation of synthesis fidelity is reduced since the generator is not included in the adversarial training. Extensive experimental results convincingly demonstrate that our proposed method is effective in avoiding message leakage and superior to other existing methods in terms of recovery robustness and synthesis fidelity.