Most existing outdoor assistive mobility solutions notify Visually Impaired People (VIP) about potential collisions but fail to provide Optimal Local Collision-Free Path Planning (OLCFPP) to enable the VIP to get out of the way effectively. In this paper, we propose MinD, the first VIP OLCFPP scheme that notifies the VIP of the shortest path required to avoid Critical Moving Objects (CMOs), like cars, motorcycles, etc. This simultaneously accounts for the VIP's mobility constraints, the different CMO types and movement patterns, and predicted collision times, conducting a safety prediction trajectory analysis of the optimal path for the VIP to move in. We implement a real-world prototype to conduct extensive outdoor experiments that record the aforementioned parameters, and this populates our simulations for evaluation against the state-of-the-art. Experimental results demonstrate that MinD outperforms the Artificial Potential Field (APF) approach in effectively planning a short collision-free route, requiring only 1.69m of movement on average, shorter than APF by 90.23%, with a 0% collision rate; adapting to the VIP's mobility limitations and provides a high safe time separation (>5.35s on average compared to APF). MinD also shows near real-time performance, with decisions taking only 0.04s processing time on a standard off-the-shelf laptop.