I started by adding Live's Vocoder and making sure the Carrier (the timbre-controlling signal) is set to "noise". The XY pad below the selector is great for changing the density and texture of the white noise, but I found only a minor tweak to this was needed in the case of these hats as I'm after the traditional white noise sound to blend with my hats.

Then it was just a matter of playing around with the settings on the device while listening at 100% wet. Since I was looking for a brighter sound with these hats, I pulled the Formants knob up so that the noise's frequencies are shifted upward.

The Depth control determines how strictly the amplitude contour of the input signal will be applied to the carrier, which can be thought of as how much influence the input signal will have on the dynamics of the carrier. I wanted to keep the noise tight with the original hat loop, so I've cranked the depth to around 136% to better match the hats' amplitude envelopes. I also set the Release to something close to the release on the hats I'm working with - a good starting place would be anywhere from 80 ms to 150 ms, but this will vary based on the original signal.