I agree with you about the source of the condensation, most likely to have been due to the machine sitting for a long while.
The problem with hydraulic oil is that like brake fluid it's hygroscopic and absorbs water, so the best way to get rid of the water is to drain the oil and that'll take the water with it.
I don't think Color Kut will work on water in hydraulic oil TBH, but I'm prepared to be proved wrong.
I personally think you won't be happy with the results of changing the tank oil + coalescing filter, etc, although on the face of it it's an extremely good idea.
Try this. Be warned it's at least a 2-man job, maybe better with 3: -
1. Drain the tank and every line that you can get to on the upper works of the machine up to & including the main control valve, so that would include the lines to/from the cooler and the pump. That should get the base machine clean-ish.
2. Every step from now on keep an eye on the tank level. It will go down and have to be topped up frequently.
3. Remove a line on the head end of each boom cylinder and drain the oil from both cylinders into a container. Refit the lines.
4. Loosen (don't remove) a line from the rod end of each boom cylinder. Start the engine and slowly raise the boom. It will take a while because the cylinders will be empty at the head end. Move the cylinders until they top out and the tighten the rod end hoses.
5. Repeat Steps 3 & 4 for the stick cylinder and the bucket cylinder.
6. Next the swing motor. Loosen a hose on one side of the motor and gently swing in that direction until you get clean oil. Tighten the connection, loosen on the opposite side of the motor and repeat for swing in the other direction.
7. Lastly the travel motors. Remove the case drain line to the tank (if fitted) at the motor end and drain the oil out into a container. Leave the case drain hoses disconnected. Loosen (don't remove) the "forward" line on one motor. Start the engine and use the implements to raise that track off the ground. Gently move the travel control to the forward position until you get clean oil coming out. At that point leave the same hose loose but put the travel control in reverse. That will bring clean oil through the return line and right through the motor. When you get clean oil tighten the connection. Repeat the process for the other track.
8. BTW. Did I mention keep an eye on the hydraulic oil level in the tank while you're doing all this .........??