The correct answer is C: Use Amazon Athena directly with Amazon S3 to run the queries as needed. Amazon Athena allows for direct querying of data stored in Amazon S3 using standard SQL syntax. It is a serverless service, meaning there is no infrastructure to manage, resulting in minimal operational overhead. Additionally, it requires no data movement and works directly with the data stored in S3. Hence, it fits the requirement of performing on-demand analysis with the least amount of changes to the existing architecture.