Recent sign language translation methods have advanced visual-language alignment, yet autoregressive generation remains vulnerable to unstable policy updates under ambiguous visual evidence. Such instability may cause locally plausible continuations to accumulate into sentence-level semantic deviations, especially when reinforcement learning is used with noisy reward and advantage estimates. Existing PPO-style policy optimization applies confidence-agnostic clipping bounds to all generated tokens, which limits its ability to distinguish between over-amplified confident predictions and low-probability tokens that may still carry useful corrective signals. To address this issue, we propose CAPO-SLT, a reinforcement learning based framework for stable sign language translation generation. CAPO introduces a confidence-aware policy optimization strategy that adapts the upper clipping bound according to old-policy token probability. It applies more conservative updates to high-confidence predictions while preserving update capacity for low-probability positive-advantage tokens. In addition, CAPO caps negative-advantage updates to improve robustness under noisy supervision. This design provides a simple drop-in replacement for standard clipping and stabilizes generation-stage optimization without changing the underlying visual encoder or reward function. Experiments on Chinese and American sign language benchmarks show consistent improvements over pose-based baselines under the same input setting, suggesting that CAPO-SLT provides an effective optimization strategy for stable sign language translation generation.