In this article, we present the dynamical analysis of the stochastic leprosy epidemic model. Positivity and boundedness are the criteria used in the deterministic model. A primary technique known as the Euler Maruyama is employed in the solution of the said model. Standard and non-standard computational methods are applied in evaluating the design stability and efficiency based on the chosen criteria. The standard computational methods like the Stochastic Euler and the Stochastic Runge Kutta fail to restore the essential features of biological problems. However, our proposed approach, the stochastic non-standard finite difference (NSFD), is used and found to be efficient, cost-effective, and accommodates all the desired feasible properties. Our method achieves all-time convergence against the backdrop of other classical techniques that perform conditionally or fail over a long period. In the end, a comparison between this scheme and the existing ones reviews the novelty of our approach.