This paper proposes a novel hybrid framework to accurately identify human peripheral blood cells. Our approach includes Big Transfer (BiT) models, combining the extracted features with classifiers: the traditional Multilayer Perceptron (MLP), the Efficient Kolmogorov-Arnold Network (EfficientKAN) and our hybrid method (HybridMLPEfficientKAN). Peripheral Blood Cell (PBC) dataset of 17092 images covering eight cell types is preferred. BiT models provide high-dimensional features for classifications pipelines. Results show that combining MLP and EfficientKAN provides strong classification accuracy while reducing training overhead often seen in standalone EfficientKAN. Training durations in HybridMLPEfficientKAN remain close to MLP training, in the range of 100-250 seconds, instead of longer durations of over 700 or even 2000 seconds in EfficientKAN. HybridMLPEfficientKAN surpasses EfficientKAN in overall accuracy, exceeding 97% in BiT models. We also evaluate class-wise performance using recall, F1-score, specificity and Matthews Correlation-Coefficient (MCC). Hybrid approach effectively balances computational cost and prediction performance, making it an attractive solution for clinical settings where classification speed and accuracy are critical. This study highlights how BiT-based feature extraction combined with carefully designed models can provide efficient PBC recognition. The integration of MLP-level efficiency with KAN-style adaptability offers a promising avenue for developing high-accuracy, low-latency cell classification systems in hematological analysis.