Having watched @aaronpk with his new quiet Hyperdeck I was curious to find out what the original fan connector is and I have found the answer, which may be of help to anyone else thinking of replacing the fan, but not wanting to cut off the original fan’s connector in case you wanted to restore it to its noisy old self.
The connector you need is a JST ZH 1.5mm Connector plug - 4 pin - with wires already attached. These are widely available on eBay and Amazon.
The fan kit that the guy on iFixit used (and Aaron I think too) is the Noctua NF-A4x20 PWM (12volt). The kit contains four Omnijoin adapters, so there is no need to solder anything! My advice is to remove most (if not all of the shielding sleeve on the new fan) so the wires fit more easily in the Hyperdeck case. Follow the wiring diagram on the iFixit page since the colour of the wires on your new connector may not match the existing fan and probably not the new fan either.
It’s a 10 minute job at most, and you can keep the original fan and connector intact in case you need to put it back.
Of course, as Aaron and iFixit point out, you do this AT YOUR OWN RISK and it will void any warranty you have.