Developing a face anti-spoofing model that meets the security requirements of clients worldwide is challenging due to the domain gap between training datasets and the diverse end-user test data. Moreover, for security and privacy reasons, it is undesirable for clients to share large amount of their face data with service providers. In this work, we introduce a novel method where the face anti-spoofing model can be adapted by the client itself to a target domain at test time using only a small sample of data, while keeping model parameters and training data inaccessible to the client. We develop a prototype-based base model and an optimal transport-guided adaptor that enable adaptation either in a light-weight training or training-free setting, without updating the base model's parameters. Moreover, we employ geodesic mixup, an optimal transport-based synthesis method that generates augmented training data along the geodesic path between source prototypes and the target data distribution. This allows training a lightweight classifier to effectively adapt to target-specific characteristics while retaining essential knowledge learned from the source domain. In cross-domain and cross-attack setting, compared with recent methods, our method achieves average improvements of 19.17\% in HTER and 8.58\% in AUC, respectively.