I found a solution, even though it is not the prettiest.
In the Spark job, before creating the SparkContext, you need to set a system property for the Hive metastore URI like so:
System.setProperty("hive.metastore.uris", "thrift://<your metastore host>:9083");
I have tried setting this through the Oozie configuration but to no avail. So far, this was the only way to make it work.