Code models have become integral to modern software development, yet they remain vulnerable to backdoor attacks through poisoned training data. Current code backdoor attacks struggle with a critical trade-off. Static triggers using fixed code patterns achieve high transferability across different settings, but are easily detected by defenses. Conversely, dynamic triggers that adapt to code context evade detection effectively but exhibit poor cross-dataset transferability. Moreover, existing dynamic approaches unrealistically assume attackers have access to victims' training data, limiting their practical applicability. To overcome these limitations, we introduce Sharpness-aware Transferable Adversarial Backdoor (STAB), a novel attack that achieves transferability and stealthiness without accessing victim data. Our key idea is that adversarial perturbations discovered in flat regions of the loss landscape transfer more effectively across datasets than those found in sharp minima. STAB leverages this by training a surrogate model with Sharpness-Aware Minimization (SAM) to guide model parameters toward these flat regions. We then employ a Gumbel-Softmax based optimization to transform the discrete search for trigger tokens into a differentiable process, generating context-aware adversarial triggers. Experiments on three datasets and two code models demonstrate the superiority of STAB. Compared to static triggers, STAB significantly improves stealiness, maintaining 73.2% average attack success rate after defense (ASR-D) versus near-zero for static approaches. In cross-dataset scenarios, STAB also outperforms the state-of-the-art dynamic attack, AFRAIDOOR, with a 12.4% higher ASR-D, while preserving model performance on clean inputs.