Although the one-dimensional continuous wavelet transform (1D-CWT) often suffers from redundant scales when applied to structural damage detection, it remains a valuable tool due to its flexibility in selecting optimal wavelet functions for improved accuracy. This paper investigates the capability of the 1D-CWT to accurately identify the most effective wavelet scales tailored for damage detection in laminated composite curved beams, a complex structural element widely used in aerospace and civil engineering. The finite element method (FEM) is utilized to obtain detailed mode shapes of these curved beams, providing representative input signals for wavelet transform analysis. To address the challenge of redundant scales, we propose employing the standard deviation of wavelet coefficients as a sensitive and robust index to pinpoint scales that most effectively highlight damage-induced changes. This quantitative metric enables a systematic selection of optimal scales, improving detection performance. Comprehensive numerical simulations complemented by experimental validations confirm that this approach significantly enhances damage localization accuracy. Overall, the results demonstrate that incorporating the standard deviation criterion into the 1D-CWT framework enhances its practicality and reliability, thereby positioning it as a powerful tool for structural health monitoring of laminated composite curved beams.