If the hiss is constant (doesn't go up or down when adjusting volume) then it's noise from the amp. If it does change then the noise is being generated upstream of the amp.
As far as the noise around cymbals and sibilants, my guess is that you're most likely picking up on distortion. Stereophile measurements seem to bear this out.
Since the Cornwalls are very efficient, my suggestion is to find an amp with a high signal to noise ratio and low distortion at the lower power output levels. Given that, an inexpensive option you might want to try is the Topping PA5.