To minimize performance impact on the currently running Cloud SQL for MySQL instance during a one-time migration to a new instance in a different region, the recommended approach is to use a SQL dump file. This method involves creating a snapshot of the data in a Cloud Storage bucket using a temporary instance, which can then be imported into the new instance. This approach is less intrusive and avoids continuous load on the source instance, unlike streaming methods. Options A and B involve more complex setups (Dataflow job and Datastream) that are better suited for continuous data replication rather than one-time migrations. Option D, while feasible, involves manual steps and potential data consistency issues, making it less ideal compared to the SQL dump method.