Can I Build a Custom Client Using the Public Server?

I'm trying to build a custom client for remote support from within our self-hosted, LAN-only server console. We choose to leave our RustDesk server not exposed to WAN in any way, but often have to help users who are remote. I know they can install the default RustDesk client from the website and I can connect from my client by using 111 222 333 @public, but I want a custom client with our logo that will default to not using our internal relay and api server. This will seem much more professional for the remote user than instructing them to go to someone else's website and install. When I try to build a custom client in my server's console, I try to leave the Relay and API fields blank, but they repopulate with my server's url. There is also a Key field that is not editable. Am I completely doing this wrong, or planning this wrong? I can't find any information about this.

Start by reviewing the existing documentation for custom clients and the server console's Relay, API, and Key fields; the issue does not identify a file, test, or entry point. Reproduce the described configuration behavior and document whether a branded client can use the public server without the internal relay and API, including the supported setup steps and limitations.