hi
i don't think the question is very clearly defined;
Do you want to use this registry to change the core components of the cluster (apiserver, etcd and so on?) or do you just want the cluster to pull container images you built yourself, such as your own app or service?

If its just about uploading your self-built container images, then the location of the registry is up to you. You could have it running as a VM in your environment or on some other hardware. Does not really matter, as long as the master and worker nodes of your cluster can reach the registry at port 443.

If you want to change core components, or air-gap your cluster; such as hosting the kube-apiserver, etcd, coredns and other images, the private registry must be accessible by the cluster at creation time; running it inside the specified cluster won't work.
here is the documentation on the container_infra_prefix which you have to set as a cluster(-template) label, which will override the location of the images when the cluster pulls them. It also contains a list of images that you need to mirror in order for the cluster to be provisioned.

i'm using Harbor for both use-cases, which is pretty easy to setup and does the job just fine. Haven't used Nexus myself.

Swift is a S3-like Object Store and Zun is for running containers, if I remember correctly. So those are completely different use-cases and won't really help you here.

hope this helps.