Controlling systems with uncertain dynamics is crucial in systems theory, especially for unmanned vehicles operating in challenging and unknown environments. One key application involves developing control methods to ensure collision-free trajectory tracking for unmanned surface vehicles (USVs) at sea. Modern control methods for such systems often encounter unwanted high-frequency oscillations, known as chattering, in the control signals. To address this, continuous approximations of discontinuous functions in the control law have proven effective in reducing chattering. This approach is integrated into a prescribed-performance control scheme, which has previously achieved asymptotic tracking for systems with uncertain dynamics. We employ Lyapunov stability analysis to determine if theoretical bounds for error performance can be smaller than the prescribed funnel functions when incorporating continuous approximations in a boundary-layer. For both first- and second-order systems, we show that system trajectories reach an arbitrarily small boundary-layer set in finite time. This allows us to derive a priori known error bounds that are smaller than the prescribed funnels. Simulations support the theoretical results, demonstrating a significant reduction in chattering while achieving asymptotic tracking errors two orders of magnitude smaller than the funnel functions.