You're able to get the current registry-url using docker info:
...
Debug Mode (server): false
Registry: https://index.docker.io/v1/
Labels:
...
That's also the url you may use to run your self hosted-registry:
docker run -d -p 5000:5000 --name registry -e REGISTRY_PROXY_REMOTEURL=https://index.docker.io registry:2
Grep & use it right away:
$ echo $(docker info | grep -oP "(?<=Registry: ).*")
https://index.docker.io/v1/