The two big ones are meant for power supply filtering and would likely mostly affect hum. To do it properly and refresh the unit, all electrolytic are suspect. Someone actually sells a recap kit for these? Interesting. There you are paying for their research time finding all the correct values and sizes. A person can also do the research themselves and buy everything from a distributer like Mouser, and pay much less.
Desoldering in my opinion is the more difficult step. As you need to leave the holes open while not lifting any pads. A desoldering iron is ideal and makes it even easier than soldering in. But not many have such a tool, I have a crude RadioShack one that uses a rubber bulb for vacuum. Solder wick will also work, but you are back to the struggle of getting the holes open. some use a small pin that can take the heat but doesn't solder well itself to keep the hole open. I have redone my own tuner, two preamps and several power amps, it can be frustrating as hell, or very therapeutic. Take some good clear photos of the board to Reference, do one cap at a time, make sure you reinstall each in the same orientation it came out.
Just remember this isn't a guarantee to fix the "farting" noise. As an electronics troubleshooter for many years this is just the next most likely action to take. For me troubleshooting by message board is not ideal. You could have a cracked solder joint or trace, a failing resistor or transistor also, but those are further down the most likely path.The fact the unit works well at times really pushes transistors far down the list at this point. Good luck.