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Federated Learning (FL) enables collaborative model training across institutions without sharing raw data. Performance degrades, however, when label distributions are imbalanced across sites, a common scenario in medical settings where disease prevalence could vary drastically across institutions. Existing distribution-aware methods rely on label distribution statistics that clients cannot share in real-world federated settings due to privacy and regulatory constraints. We propose FedSwitch, a model-agnostic FL framework that estimates the global label histogram, under client-level epsilon-differential privacy, and uses the estimate to switch from FedAvg to distribution-aware aggregation. Each client adds partial discrete Laplace noise to its bounded label counts and secret-shares the result via Shamir’s scheme, designated decryptors reconstruct the noisy aggregate without ever observing individual contributions. The optimal switching round can be estimated via a closed-form variance decomposition that accounts for bounded contributions, client sampling, and differential-privacy noise components. We evaluate FedSwitch on medical imaging benchmarks under realistic heterogeneous settings, demonstrating consistent improvements over standard FL aggregation with negligible communication overhead.