A quantum channel is a physical media able to carry quantum signals. Quantum key distribution (QKD) requires direct quantum channels between every pair of prepare-and-measure modules. This requirement heavily compromises the scalability of networks of directly connected QKD modules. A way to avoid this problem is to introduce switches that can dynamically reconfigure the set of connections. The reconfiguration of a quantum channel implies that the modules using it can adapt to the new channel and peer.The maturity and flexibility of continuous-variable QKD (CV-QKD) qualifies it as a strong contender for integration into optical communication networks. Here we present the implementation of a switched CV-QKD network embedded in the Madrid quantum testbed. The optical switching of the quantum paths significantly reduces the amount of required QKD modules and facilitates the scalability of the network. This demonstration highlights the flexibility and ease of integration of this emerging technology.