The engineering of exceptional points (EP) in gain-loss-assisted optical systems has recently garnered considerable attention for the development of unconventional photonic components. Moreover, the substantial noise associated with EPs poses a significant challenge to realizing their full potential in applications. There is a gap in the exploration of asymmetric mode conversion phenomena in the close proximity of the dynamical encirclement around an EP. In response, we propose the design of a fabrication-feasible dual-mode optical planar waveguide. Non-Hermiticity, in terms of a customized gain-loss profile, is introduced to modulate the interaction between the coupled modes. Contrary to previous assumptions, we establish that the dynamical encirclement of an EP is not a prerequisite for achieving asymmetric mode conversion. Furthermore, we calculate the Petermann factor (K) near the EP and demonstrate a significant two orders of magnitude reduction in the Petermann noise factor when we do not dynamically encircle the EP. Hence, we propose a new scheme to reduce the inherent noise.