Background: Early risk stratification of febrile neutropenia (FN) in the emergency department (ED) is vital to accelerate empirical antibiotic management. This study evaluates the independent diagnostic performance of combined blood-borne inflammatory indices and the Shock Index (SI) in predicting FN status and severe clinical outcomes. Methods: Medical records of 338 febrile oncology patients presenting to the ED between 2020 and 2026 were retrospectively evaluated. Patients were divided into the FN group (fever + ANC < 1000 cells/μL; n = 213) and the control group (n = 125). Advanced cell-line metrics and biochemical ratios were calculated at admission. Independent predictors were isolated using multivariable logistic regression analysis. Results: Multivariable regression analysis revealed that elevated core body temperature (aOR: 3.229, 95% CI: 1.845–5.652, p < 0.001), lower serum sodium levels (aOR: 0.843, 95% CI: 0.767–0.926, p < 0.001), a low Neutrophil-to-Lymphocyte Ratio (NLR) (aOR: 0.636, 95% CI: 0.549–0.736, p < 0.001), and an elevated Shock Index (aOR: 24.010, 95% CI: 2.258–255.360, p = 0.008) were stable independent predictors of FN. The combined four-variable integrated model achieved an outstanding Area Under the Curve (AUC) of 0.906 (95% CI: 0.874–0.937) with a diagnostic sensitivity of 77.4% and a specificity of 87.0%. Conclusions: Integrating baseline core temperature, hyponatremia, low cellular NLR, and physiologic SI values creates a rapid, cost-effective, and highly accurate screening platform to optimize emergency triage workflows and prevent computational delivery latency in critical oncologic emergencies.