The success or failure of modern computer-assisted surgery procedures hinges on the precise six-degree-of-freedom (6DoF) position and orientation (pose) estimation of tracked instruments and tissue. In this paper, we present HMD-EgoPose, a single-shot learning-based approach to hand and object pose estimation and demonstrate state-of-the-art performance on a benchmark dataset for monocular red-green-blue (RGB) 6DoF marker-less hand and surgical instrument pose tracking. Further, we reveal the capacity of our HMD-EgoPose framework for 6DoF near real-time pose estimation on a commercially available optical see-through head-mounted display (OST-HMD) through a low-latency streaming approach. Our framework utilized an efficient convolutional neural network (CNN) backbone for multi-scale feature extraction and a set of subnetworks to jointly learn the 6DoF pose representation of the rigid surgical drill instrument and the grasping orientation of the hand of a user. To make our approach accessible to a commercially available OST-HMD, the Microsoft HoloLens 2, we created a pipeline for low-latency video and data communication with a high-performance computing workstation capable of optimized network inference. HMD-EgoPose outperformed current state-of-the-art approaches on a benchmark dataset for surgical tool pose estimation, achieving an average tool 3D vertex error of 11.0 mm on real data and furthering the progress towards a clinically viable marker-free tracking strategy. Through our low-latency streaming approach, we achieved a round trip latency of 202.5 ms for pose estimation and augmented visualization of the tracked model when integrated with the OST-HMD. Our single-shot learned approach was robust to occlusion and complex surfaces and improved on current state-of-the-art approaches to marker-less tool and hand pose estimation.