Internet of Things (IoT) services deployed across different Cloud Service Providers (CSPs) require seamless migration across heterogeneous clouds. Sky Computing (SC) facilitates the requirement by implementing a coordinator with communication APIs among clouds. However, security concerns of CSPs prevent the coordinator from accessing detailed cloud hardware information, thereby hindering the assessment of Serving Ability (SA) and exacerbating delays in service delivery. To ensure delay experience, we designed a loss-aware coordinator SkyCap for the multi-CSP collaboration in SC. First, to assess the SA of clouds with available information, we design a loss-aware SA assessment mechanism AdaSA that collects delay experience and Packet Loss Ratio (PLR) information for SA assessment. Since the uncontrollable PLR can increase service delay, we incorporate PLR as a disturbing factor in SA assessment to ensure a more precise evaluation. Second, to maximize the admission profit of the collaboration, we design two approximation algorithms within SkyCap to serve requests. Since the coordinator may deploy services in batches, we design a delay-aware offline algorithm AdaOff to serve requests simultaneously, while ensuring the computing capacity of clouds and the delay requirement of requests. Meanwhile, for asynchronously arriving requests, we design an ability-aware online algorithm AdaOn to serve requests in real-time, while guaranteeing the computing capacity of clouds, SA of clouds, and delay requirement of requests. Finally, extensive theoretical analysis and experimental validation confirm the performance of the coordinator SkyCap. The SA assessment mechanism AdaSA outperforms existing solutions in SA assessment by ensuring at most 1% deviation, especially in high-PLR scenarios. Meanwhile, the algorithm AdaOff exhibits a remarkable 20% improvement over the state-of-the-art in admission profit while ensuring stringent service delay. Concurrently, the algorithm AdaOn surpasses existing solutions, achieving a nearly 10% enhancement in both admission profit and service delay. In summary, the coordinator SkyCap stands out in theoretical groundwork and practical implementation, offering advancements in the SA assessment, admission profit, and service delay.