I would only make cuts if I found it difficult to hear elements clearly and as distinct sounds (regardless of the frequency range). I would more than likely make any necessary cuts on the white noise as opposed to the hi hats. This varies with the type of music your working on, but hi hats are essential to rhythms a lot of the time. Removing them or cutting them too much might subtract from the overall grove if they end up sounding bad or lackluster. On the other hand, noise is usually an effect that has a very wide range. Cuts in the high end won't be as drastic here as would be the case for hats. Also, you could get away with some stereo widening effects to help white noise be more distinct in a mix.
With all that said, I've never had an issue of white noise clashing with a high hat, cymbal, or other high frequency sounds. White noise is fairly quiet in my tracks since it is very fatiguing and annoying for me to listen to at louder levels.