Accurate boundary delineation in medical ultrasound (US) images remains challenging because of speckle noise, low contrast, acoustic shadowing, and acquisition variability. We propose Risk-routed Implicit Boundary Refinement (RIBR), a compact framework that refines convolutional segmentation through spatially weighted implicit residuals. A coordinate-conditioned implicit branch uses regional features to predict logit corrections, and a learned gate controls their contribution using predictive uncertainty and local appearance. Geometry- and speckle-aware regularization provides contour supervision and discourages probability fluctuations away from boundaries. We compare RIBR with ten baselines on nine datasets covering lymph nodes, breast lesions, thyroid nodules, and prostate, including four external lymph-node and breast cohorts. Across three seeds, RIBR achieves the best overall dataset macro-average among the evaluated configurations, with $76.67{\pm}0.42\%$ Dice and a 95th-percentile Hausdorff distance (HD95) of $29.55{\pm}0.55$ pixels on the resized evaluation grid. It obtains the lowest HD95 on all nine datasets, with task-dependent Dice rankings. These results support controlled implicit residual refinement for boundary-sensitive US segmentation. Source code is available at https://github.com/jinggqu/ribr.

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