Carb parts needed for Kohler Courage 20

My brother has conned me into working on his mower and I'm having problems trying to find the parts I need. The fuel cutoff solenoid needs to be replaced as well as the float needle. The only thing I can find are complete carburetors. Do they sell these parts individually or is a new carb purchase required? In my searches I've seen where several different carbs are listed and all appear to be for this same motor. If it takes a full carb replacement, is there one (such as a Walbro model) that is preferred over the others?

Engine info

Family 8KHXS.5972GB
Type APP e11*97/68SA*2002/88*0285*01
CC 597
Model # SV600S
Spec # SV-600-0024
Build Date 2008

Any help is very much appreciated.