After I replaced my leaky windows I was left with similar discolored veneer. I purchased thin sheets of teak veneer on the Internet. I then made a pattern out of thin cardboard and used the patterns to cut the veneer to fit (it doesn't have to fit perfectly). Then I used Titebond glue and painted both the old surface and the back of the veneer and let the two surfaces dry.
Then having plenty of time to position the piece I then applied a hot clothing iron from the center to the edges. That will melt the glue and bond the parts. This is reversible if you screw up.
Finally I used a single coat of Cetol natural teak and a coat of clear. This worked for me, you might need to experiment with some scrap veneer to get a good match.