Yes, deploy WireMock as a container and route your request to that container. You could do that by deploying a DNS and manipulate that.
Easier would be if you can use change the endpoint in your application directly, do your testing and change to the real thing when you're done.
But I would probably go for using a custom DNS that will route the endpoint, say
api.extservice.com to your container's IP address. When all is working fine, you can change it back to the real IP