Recent progress in zero-shot 6D object pose estimation has been driven largely by large-scale models and cloud-based inference. However, these approaches often introduce high latency, elevated energy consumption, and deployment risks related to connectivity, cost, and data governance; factors that conflict with the practical constraints of real-world robotics, where compute is limited and on-device inference is frequently required. We introduce Geo6DPose, a lightweight, fully local, and training-free pipeline for zero-shot 6D pose estimation that trades model scale for geometric reliability. Our method combines foundation model visual features with a geometric filtering strategy: Similarity maps are computed between onboarded template DINO descriptors and scene patches, and mutual correspondences are established by projecting scene patch centers to 3D and template descriptors to the object model coordinate system. Final poses are recovered via correspondence-driven RANSAC and ranked using a weighted geometric alignment metric that jointly accounts for reprojection consistency and spatial support, improving robustness to noise, clutter, and partial visibility. Geo6DPose achieves sub-second inference on a single commodity GPU while matching the average recall of significantly larger zero-shot baselines (53.7 AR, 1.08 FPS). It requires no training, fine-tuning, or network access, and remains compatible with evolving foundation backbones, advancing practical, fully local 6D perception for robotic deployment.