Low Earth orbit (LEO) satellite constellations are emerging as a key enabler of next-generation communications, offering global coverage and significantly lower latency compared to traditional terrestrial networks and geostationary satellites. However, further latency reduction is essential for time-critical applications such as real-time sensing, autonomous systems, and interactive services. One critical bottleneck is the optical-to-electrical (O/E) and electrical-to-optical (E/O) conversions at intermediate nodes in multi-hop links, which introduce unwanted processing delays. To address this, we investigate an all-optical relay system based on Optical Hard Limiters (OHL), which operate purely in the optical domain to suppress noise and restore signal quality without requiring O/E conversions. First, we present a rigorous analysis of inter-satellite multi-relay communication under the OHL relaying architecture, comparing it against conventional Amplify-and-Forward (AF) and Decode-and-Forward (DF) schemes. Through this comparison, we highlight both the advantages and limitations of OHL relays, including their particular sensitivity to parameter choices such as the threshold setting and divergence angle at the transmitter. Recognizing that a LEO constellation is inherently time-varying - satellites move relative to one another, causing continuous changes in link distances and tracking errors - we propose a joint optimization strategy. This scheme adaptively tunes the OHL decision threshold and beam divergence in real time to maintain optimal performance, ultimately lowering error rates and latency. Extensive simulations in a large-scale LEO network demonstrate the viability of our method and offer insights into practical implementation for next-generation inter-satellite communication systems.