Network administrators usually realize network functions in data plane programs. They employ the network-wide program deployment that decomposes input programs into match-action tables (MATs) while deploying each MAT on a specific switch. Since MATs may be deployed on different switches, existing solutions propose the inter-switch coordination that uses the per-packet header space to deliver crucial packet processing information among switches. However, such coordination incurs non-trivial per-packet byte overhead, leading to end-to-end performance degradation. We propose Hermes, a framework that aims to minimize the per-packet byte overhead. The key idea is to formulate network-wide program deployment as a mixed-integer programming (MIP) problem with the objective of minimizing the per-packet byte overhead. Also, Hermes offers a greedy-based heuristic that solves the problem in a near-optimal and timely manner. We have implemented Hermes on Tofino switches. Compared to existing frameworks, Hermes decreases the per-packet byte overhead by 156bytes while preserving end-to-end performance in terms of flow completion time and goodput.