By the time I created this I should have done some research. Here is a better idea, if you're anyhow using nginx in front of the service:
Set up your own what is my ip service with just nginx
A deployment of WhatsMyIP:
This tool is a very simple HTTP Server: It returns the REMOTE_ADDR to connecting HTTP clients. In other words: It tells you what your current IP is.
The container will expose the HTTP Port 8080 and respect the header X-Real-IP that can be added by your reverse proxy.