and then in your browser just type the letter you assign it to: for example, I have 'i' == the searchbox for IMDB, so I type 'i [movie]' in my url and it brings up the IMDB search of that movie . https://i.imgur.com/dXdwsbA.png
So you can just assign 'a' to that search box and type 'a [URL]' in your address bar and it will submit it to your little thing.
If the install is under "eixk3.somedomain.com/ladderforfriends" and it sits behind a reverse proxy, it might as well be invisible to the internet, unless your DNS provider is an idiot and allows zone transfers, or you are on a network where someone is snarfing up DNS requests and then distributing that info to third parties. If you restrict it to TLS 1.3, even someone sniffing traffic from one of your friends won't be able to glean anything useful, because the requested hostname is never sent in plaintext.
Rotate the hostname if/when it becomes necessary...
You could mitigate that with a wildcard cert, but still..