I'm trying to see if it's possible to use the Prince Docker image for converting XML to PDF from a C# program in a container. The C# wrapper is asking for the path to the executable, but would it work if I passed the path based on where the image has been mounted in the container?

The C# wrapper calls the Prince shell script with the necessary arguments, so "prince [ARGS]", so you could point it at a shell script you have written to invoke Prince in Docker instead.