Channel knowledge maps (CKMs) provide a site-specific, location-indexed knowledge base that supports environment-aware communications and sensing in 6G networks. In practical deployments, CKM observations are often noisy and irregular due to coverage-induced sparsity and hardware-induced linear/nonlinear degradations. Conventional end-to-end algorithms couple CKM prior information with task- and device-specific observations, and require labeled data and separate training for each construction configuration, which is expensive and therefore incompatible with scalable edge deployments. Motivated by the trends toward cloud-edge collaboration and the Artificial Intelligence - Radio Access Network (AI-RAN) paradigm, we develop a cloud-edge collaborative framework for scalable CKM construction, which enables knowledge sharing across tasks, devices, and regions by explicitly decoupling a generalizable CKM prior from the information provided by local observations. A foundation model is trained once in the cloud using unlabeled data to learn a generalizable CKM prior. During inference, edge nodes combine the shared prior with local observations. Experiments on the CKMImageNet dataset show that the proposed method achieves competitive construction accuracy while substantially reducing training cost and data requirements, mitigating negative transfer, and offering clear advantages in generalization and deployment scalability.