There are 2 kinds of teak cleaner sold at most marine stores. The 1 part cleaner is mostly Oxalic acid which would not be great for metals if left on a long time. The 2 part cleaner is an even stronger potion.
Can you remove any of the teak for treatment?
In my limited experience with the teak 'brighteners' I think they work moderately well.
I would lightly sand the surfaces of the teak, oil it with teak oil and let it soak in for a day. Before applying your finish wipe the wood down with acetone.
If you are going to use Cetol make sure to get the 'Natural Teak' variety. It almost looks like varnish and is nicer then the orangey 'Cetol Marine'.
My $.02

 

We used Star Brite teak cleaner on our boat and were very happy with the results. There was no metal to worry about, but we did get some on the deck. We anticipated this, so as my better half applied the cleaner to the teak, I watched for any runoff. When I saw some, I quickly rinsed it off and soaked up the water with a rag. I would do this repeatedly, hopefully removing all the acid, or at least diluting it significantly. There was no damage to the deck. I'm not sure if this was a good idea, but it seemed to work for us. I should also say that we had no black rot to deal with, only gray weathered teak. Best of luck.

 

I used the star brite kit as well. My wood was off the boat, but I was very pleased with the results. I can tell you that the "brightener" is at least 90% bleach. Still, good stuff.