Despite their illegality, untethered free-floating naval mines are increasingly employed as part of maritime area-denial operations. By ignoring international treaties, these mines require less effort to acquire and deploy, and result in a far more dynamic-threat environment. In order to assist commanders during breach operation planning, we develop several algorithms that generate a minimum-risk journey through a field of drifting mines. Using Voronoi graphs to capture a series of static snapshots of the operational area, we present a practical methodology for building a fully connected time-varying graph (, ). Vertices are defined as specific times and locations, and edges define the continuous movement of a ship with simple parametric equations. The length, acceleration and risk of each edge is calculated and employed by a threat-additive A * search to quickly find a plausible, minimum-risk journey through a given minefield within a specific time frame. Using real-world data for a modern-day port and minefields of variable density, we find navigable paths that incur acceptable risk in less than 2 minutes on average. We also introduce several methods for reducing the size of (, ) and the time required for its generation.