You can use the SPICE noise models of the circuit elements and run SPICE noise analysis to get the noise across the hold capacitance. This is the solution method.
The noise generated in the devices and circuits are direct thermal noise and shot noise in electronic devices which is also stems from thermal velocity randomness of the charge carries. In fact you have to consider all types of noise when you study the effect of noise on the sample and hold circuit. All types of noise will affect the behavior the circuit. So, you have to consider them all.
There are other types of noise which are caused by man made noise as interference signal.