I would never use a pressure washer on my deck - not even a strong spray from a hose sprayer. I use a chamois headed mop and then for tough spots a very soft brush. And I always wipe across the grain to avoid eroding the softer wood that runs between the grain.
I have used Joy but for the last several years I've been using the cleaner from Teak Decking Systems in Florida
. These guys build teak decks for superyachts and cruise
ships. The cleaner does just what you are looking for - it makes the teak whiter not browner by pulling all of the black mildew and dirt out of the grain. Their description says:
Teak Cleaner Liquid is designed to be gentle to your teak, caulking, hardware or paint. Teak Cleaner Liquid is water-based, contains no acids and is designed not to harm the environment.
I don't wear gloves. It also doesn't seem to hurt stainless, aluminum
They have a powder and a liquid. The powder is designed to be used weekly! (I guess that's an advantage of having a cruise ship
crew). The liquid is supposed to be used monthly but I get by with twice a year. I also keep some premixed in a little spray bottle for the occasional spot. I buy mine at Jamestown Distributors.