Finite-time Lyapunov exponents (FTLEs) are widely used to identify Lagrangian coherent structures (LCS) in geophysical flows. Applying FTLEs to numerical model output requires reconstructing continuous velocity fields from discrete model grids, thus the resulting flow structures are sensitive to the interpolation method. This issue is particularly important for models with staggered-grid discretisations and complex solid boundaries, such as buildings, terrain and coastlines, where velocity components are defined at different locations and no-through-flow conditions must be respected. Most existing FTLE workflows assume co-located velocity components and do not explicitly account for fluid-solid boundaries during interpolation. Interpolating staggered velocities to cell centres before trajectory integration can therefore violate boundary conditions, producing unphysical particle paths, including trajectories that enter solid regions. Here, we present a flux-conservative, mimetic vector interpolation scheme that removes the co-location assumption while ensuring no-through-flow conditions at fluid-solid interfaces. We demonstrate the method using large eddy simulations of a wildfire plume in urban terrain. Compared with conventional interpolation, the mimetic approach produces boundary-aware trajectories and reveals coherent-structure geometries shaped by urban topography that are otherwise obscured. These results show that interpolation is not merely a numerical preprocessing step, but can directly affect inferred LCS geometries and their physical interpretation in staggered-grid simulations with complex boundaries.