The present paper proposes a bayesian approach for wavelet shrinkage with the use of a shrinkage prior based on the generalized secant hyperbolic distribution symmetric around zero in a nonparemetric regression problem. This shrinkage prior allows the control of the kurtosis of the coefficients distribution, which impacts on the level of shrinkage on its extreme values. Statistical properties such as bias, variance, classical and bayesian risks of the rule are analyzed and performances of the proposed rule are obtained in simulations studies involving generated wavelet coefficients from different kurtosis values and the Donoho-Johnstone test functions. Application of the proposed shrinker in denoising Brazilian stock market dataset is also provided.