What external HDD case is this in? Single HDD? A single HDD does not need much airflow, some enclosures are passively cooled. I wonder if you can just mount a far more common axial fan instead, even if it requires drilling new mounting holes or modifying the case, presuming the warranty has expired on the product (or else get it replaced under warranty).
This type of fan tends to get quite noisy at higher RPMs, I would not want a 1W or higher version of it, plus with the higher RPM it will wear out that much faster. You can "probably" greatly extend the lifespan of such sleeve bearing fans by periodically lubing them with a drop of light weight oil, provided they have a rubber bung seal instead of the newer design some fans have which has no access to the bearing/bushing.
You could trace the circuit to determine if there are any power limitations. Is it always on at constant speed or does speed vary with temperature or it shuts off when the HDD goes into sleep mode? You can compare the current spec of the PSU, subtract the current spec of the HDD, and see how much current reserve there is, though running the PSU at higher current will wear it out faster too, particularly if a typical sealed AC/DC plastic brick.
That is a basic two wire brushless fan, with a starting voltage of 8V (see linked datasheet below). You could "probably" get the higher power version and merely put some silicon diodes in series to drop voltage or a 2W, few dozen ohms resistor in series to limit current and thus power and RPM.
https://media.digikey.com/pdf/Data Sheets/Sunon PDFs/GB1205PHV3-8AY.GN.pdf
Here is one alternative I see with a 0.72W rating, and ball bearing so may be longer lasting, but more importantly, much lower cost than the listings for the Sunon, without being the generic junk I saw at higher wattage on Amazon. With any of them you may have to solder the correct connector on:
https://www.arrow.com/en/products/bm5115-04w-b30-l00/minebeamitsumi-inc
If you do a google search for that NMB fan model # you will find it at several merchants including Amazon (3rd party seller):
https://www.google.com/search?q=BM5115-04W-B30-L00
https://www.amazon.com/NMB-TECHNOLOGIES-BM5115-04W-B30-L00-Blower-15MM/dp/B00DRDTAMQ
I leave it to you to determine if the above
suggestion is dimensionally identical, it is a somewhat standard size but an alteration of the case or different mounting screws might be needed.
