The training efficacy of finger vein models is influenced by varied device image acquisition characteristics, collector gestures, and contact modes. However, conventional approaches relying on vast data volumes face challenges in the finger vein domain due to stringent security and privacy concerns, limiting data availability. This study proposes a federal learning framework for vein recognition model training, introducing FedFvMCo, a model of contrastive learning among participants. By comparing global and local lightweight model parameters under data convergence limitations, FedFvMCo enhances cross-domain finger vein recognition performance and model generalization. Incorporating an attention mechanism into the lightweight model further optimizes its application in resource-constrained intelligent devices. This framework is validated using four public datasets, demonstrating improved model performance and independence from data convergence constraints. This method can be extended to different modes of biometrics recognition.