This is basically what Xray [1] does. For any connection request matching a particular SNI and not presenting a secret key, it proxies the entire SSL handshake and data to a camouflage website. Otherwise it can be used as a regular proxy disguised as SSL traffic to that website (with the camouflage website being set as the SNI host, so for all purposes legit traffic to that host for an external observer).
It's meant to get around the great firewall in China, so it has to avoid the GFW's active probers that check to make sure the external website is a (legit) host. However a friend was able to get it to work American's in-flight firewall if the proxy SNI is set to Google Analytics.
Someone was using Xray, proxying to my employer, and it was detected in our attack surface management tool (Censys). I had some quite stressful few minutes before I realised what was going on, "how the hell have our TLS cert leaked to some random VPS hoster in Vietnam!?".
Thankfully for my blood pressure, whoever had set it up had left some kind of management portal accessible on a random high port number and it contained some strings which led me back to the Xray project.
It's meant to get around the great firewall in China, so it has to avoid the GFW's active probers that check to make sure the external website is a (legit) host. However a friend was able to get it to work American's in-flight firewall if the proxy SNI is set to Google Analytics.
[1] https://github.com/XTLS/Xray-core