Latency-sensitive embedded applications increasingly rely on edge computing, yet dynamic network congestion in multi-server architectures challenges proper edge server selection. This paper proposes a lightweight server-selection method for edge applications that fuses latency prediction with adaptive reliability and hysteresis-based handover. Using passive measurements (arrival rate, utilization, payload size) and an exponentially modulated rational delay model, the proposed Moderate Handover (MO-HAN) method computes a score that balances predicted latency and reliability to ensure handovers occur only when the expected gain is meaningful and maintain reduced end-to-end latency. Results show that MO-HAN consistently outperforms static and fair-distribution baselines by lowering mean and tail latencies, while reducing handovers by nearly 50% compared to pure opportunistic selection. These gains arise without intrusive instrumentation or heavy learning infrastructure, making MO-HAN practical for resource-constrained embedded devices.