The use of HSI for autonomous navigation is a promising research field aimed at improving the accuracy and robustness of detection, tracking, and scene understanding systems based on vision sensors. Combining advanced computer algorithms, such as DNNs, with small-size snapshot HSI cameras enhances the reliability of these systems. HSI overcomes intrinsic limitations of greyscale and RGB imaging in depicting physical properties of targets, particularly regarding spectral reflectance and metamerism. Despite promising results in HSI-based vision developments, safety-critical systems like ADS demand strict constraints on latency, resource consumption, and security, motivating the shift of ML workloads to edge platforms. This involves a thorough software/hardware co-design scheme to distribute and optimize the tasks efficiently among the limited resources of computing platforms. With respect to inference, the over-parameterized nature of DNNs poses significant computational challenges for real-time on-the-edge deployment. In addition, the intensive data preprocessing required by HSI, which is frequently overlooked, must be carefully managed in terms of memory arrangement and inter-task communication to enable an efficient integrated pipeline design on a SoC. This work presents a set of optimization techniques for the practical co-design of a DNN-based HSI segmentation processor deployed on a FPGA-based SoC targeted at ADS, including key optimizations such as functional software/hardware task distribution, hardware-aware preprocessing, ML model compression, and a complete pipelined deployment. Applied compression techniques significantly reduce the complexity of the designed DNN to 24.34% of the original operations and to 1.02% of the original number of parameters, achieving a 2.86x speed-up in the inference task without noticeable degradation of the segmentation accuracy.