Replacing PSU fan with a Noctua. Is this okay?

First off, I know that opening a PSU is dangerous. I'm an electrical engineer and I'm using shock-proof tools and taking the proper precautions before and after opening the unit.

Despite being only 1 year old, the PSU in my wife's PC (Thermaltake Toughpower SFX 850W) started making a loud squeaking noise whenever the fans ran, so I bought a Noctua NF-A9x14 PWM fan to replace the stock fan with. The fan fits just fine, but it's a 4-pin fan and the stock fan is 2-pin. I would think this is just 12V and GND pins and the stock fan is either at 100% or 0% and just turns on and off, but according to the website, it has a fan curve graph which would indicate variable speed. Also, the stock fan was only squeaking while idle so that would suggest it's variable.

I found the pinout for noctua fans, and the connector fits if I plug in the new fan to just the 12V and GND connectors on the PSU. The problem with this is that the fan doesn't run immediately, and I've found some other posts saying that PWM fans have a higher base voltage requirement and the PSU won't activate the fan until it reaches higher on the fan curve than it would normally.

Does anyone have experience replacing a fan like this? Should the new fan be connected to the 12V and GND pins or do I need the signal pin? If it's 12V and GND is it bad for the PSU to have a higher fan curve like that?