This is exactly what the Maven Shade Plugin is designed for. Unfortunately this plugin expects that all of your separate jar files are already present in the Maven repository as individual artefacts. Doh!
I didn't want to have all of the 16 separate jar files in the project Maven repository. I just wanted one artefact, the client that I needed to access the API. So I needed a way around Shade's dependency requirement.
My solution was to use a shell script to do some of the work, then to leverage my local Maven repository before deploying to the hosted project Maven repository. So lets see what I did exactly -
First I put all of the separate jar files that made up the 'API client' into a directory.
Then I wrote a simple shell script that did two things - 1) install all of the jar files from the client_jars directory into my local Maven repository, and 2) created a pom.xml file with Maven Shade configuration to generate the uber jar file and its dependency reduced pom.
Here's what the script looked like: