Calling a private service behind a cloudflared tunnel

I currently have service running in a private VPC on AWS that I want to talk to from CloudFlare Workers. So I set up a cloudflared tunnel to it. I got everything working by setting up a public hostname and protecting it with a "Self-Hosted" Application using aa service auth token.

However I'm a bit uncomfortable with having a public DNS record (even if it's technically protected by the Application policies). e.g. what if someone accidentally deletes the Application?

Is it possible to get rid of the public hostname altogether and call the *.cfargotunnel.com address directly from Workers?
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