With the advent of interconnected and sensor-equipped edge devices, Federated Learning (FL) has gained significant attention, enabling decentralized learning while maintaining data privacy. However, FL faces two challenges in real-world tasks: expensive data labeling and domain shift between source and target samples. In this paper, we introduce a privacy-preserving, resource-efficient FL concept for client adaptation in hardware-constrained environments. Our approach includes server model pre-training on source data and subsequent fine-tuning on target data via low-end clients. The local client adaptation process is streamlined by probabilistic mixing of instance-level feature statistics approximated from source and target domain data. The adapted parameters are transferred back to the central server and globally aggregated. Preliminary results indicate that our method reduces computational and transmission costs while maintaining competitive performance on downstream tasks.