I wouldn't touch those pins! They will oxidize slightly, but the zif socket grabs them tight enough that oxidation isn't an issue.
They have a gold plating so shouldn't oxidize easily. Static discharge, however, is another matter.
This hardware really isn't designed for frequent disassembly and reassemble. Parts are way to fragile and to many ways for things to fail. Just assemble it and leave it assembled. Even if the thermal compound is dried it will perform well enough so unseating a cooler just for that shouldn't be necessary unless it was dislodged by careless dusting. Movement of the heatsink or waterblock can crack dried compound and that's when thermal transfer is adversely affected.
Thermal compound and dust on the pins shouldn't impede performance, I'd leave it. Unless it is liquid metal...then it's probably a binner anyways. I'm not sure even ultrasonic bath cleaning could get that out reliably.