You're free to use a different router on the Cuckoo network. However:
When you Signup to Cuckoo you have the option to use your own router. This is great for the environment if you don't need one as it reduces technology waste ♻️.
Double-check that your router will be compatible with the Cuckoo network. Some ISPs 'lock' their routers to their network, which means they can't be used elsewhere. If you have any doubts, double-check by getting in touch with your existing provider.