There is a nice tool called multirust to manage multiple installs of rust which looks at manifests from the static-rust-lang-org.s3/…/dist/ directory do decide if it needs an update.
If you’re okay with the multirust way of doing things (it installs a proxy script that calls out to rustc, cargo for you) it’s totally transparent and quite nice. I recommend it. I often run multirust update nightly to be told I’m already on the latest version after a very quick manifest check. It has lots of other nice features too, but I’m basically using it as my rustup.sh replacement.