TCP congestion control is a vital component for the latency of Web services. In practice, a single congestion control mechanism is often used to handle all TCP connections on a Web server, e.g., Cubic for Linux by default. Considering complex and ever-changing networking environment, the default congestion control may not always be the most suitable one. Adjusting congestion control to meet different networking scenarios usually requires modification of TCP stacks on a server. This is difficult, if not impossible, due to various operating system and application configurations on production servers. In this paper, we propose Mystique, a light-weight, flexible, and dynamic congestion control switching scheme that allows network or server administrators to deploy any congestion control schemes transparently without modifying existing TCP stacks on servers. We have implemented Mystique in Open vSwitch (OVS) and conducted extensive test-bed experiments in both public and private cloud environments. Experiment results have demonstrated that Mystique is able to effectively adapt to varying network conditions, and can always employ the most suitable congestion control for each TCP connection. More specifically, Mystique can significantly reduce latency by 18.13% on average when compared with individual congestion controls.