From the DESCRIPTION paragraph of man hdparm:
hdparm provides a command line interface to various kernel interfaces supported by the Linux SATA/PATA/SAS "libata" subsystem and the older IDE driver subsystem. Many newer (2008 and later) USB drive enclosures now also support "SAT" (SCSI-ATA Command Translation) and therefore may also work with hdparm. E.g. recent WD "Passport" models and recent NexStar-3 enclosures. Some options may work correctly only with the latest kernels.
So yes, hdparm will work with some external HDDs: basically all eSATA HDDs and those USB HDDs which are using SCSI-ATA Command Translation.
For specifically Western Digital HDDs, there is also the idle3-tools package. If you can read the SMART information from your WD external drive, then idle3-tools should also work.
And it's likely you could take the drive out of the enclosure, plug it into an internal SATA cable, use hdparm to change its settings persistently, and then place it back into the external enclosure. Of course that voids the warranty, if you care about that...