Some good information was posted earlier - again, make sure that the capsule is actually the problem. Also consider that if a bias resistor is dirty, it too may quiet down when the mike is dried. So, it may be worth cleaning the components directly attached to the capsule and the impedance converter circuit, if only because that's generally a lot easier and safer to do. Then, dry the mike and see what problems remain.
Another idea is that the diaphragm itself may not need to be cleaned directly. If the sputtered metal is on the outer surface of the diaphragm, then it is already conductive (and needs to stay that way). What you could do instead is to clean the insulators that separate the diaphragm and electrodes, since this is where the bias voltage is present, and it's where there needs to be extremely low leakage. These parts are usually at the periphery of the capsule, and also possibly the mounting post or clamp.
The danger is that if you get any fluid in any of the capsule breather holes and it gets drawn inside of the capsule by capillary forces, the fluid will slowly evaporate and build up pressure inside of the capsule, swelling the diaphragm and probably destroying it. You can guess how I figured this out! :-/
So, the cleaning process is still not such a safe or simple procedure, but since the insulators are the primary item to keep clean, you can generally avoid cleaning the diaphragm itself. Of course, some mikes that have been used without a windscreen can have a lot of dried spittle on the diaphragm, changing its mass. Those diaphragms can be cleaned, but you run the risk of destroying the capsule if you're careless.
I'd try to read as many accounts of capsule cleaning as you can, but the general idea is to use an ultra-clean solvent and an ultra-clean applicator. Apply the solvent sparingly to the applicator and apply extremely little pressure while you move it around the surface. I've used cotton swabs that I've pulled the fibers away from the stick, then rinsed it with clean solvent, and then gently applied it to the capsule, allowing surface tension and not deliberate pressure to guide it along the surface you want to clean. Work slowly and make sure that solvent can't run into the capsule as mentioned above. Best of luck!