If I understand this correctly;
You don't need to integrate an external webservice API on your moodle end.
IE: the outside system is not communicating with moodle to retrieve the completion data.
You are passing the completion data to (outside system) API
What seems to be needed is a simple event trigger that checks for the occurrence of a course being flagged as completed then firing off the relevant information to the external system.
Overall; fairly simple and straight forward, development time is minimal, the only real question is "can moodle provide all the information the third party api is expecting".
The string provided above is not very helpful if that is an example of the data they are expecting to receive.
If you can't find a developer, feel free to contact me privately.