I just finished refinishing some old 1970's kitchen cabinets I had stored away for a basement kitchenette. I kept them because I thought they were well built with solid wood doors with plywood boxes. I was surprised to find that the inner panel of the door was a veneer. I realized it after I had used a gentle citrus stripper on it and the dark stain was removed. I was able to gently sand and stain it and it came out well - I restrained it walnut, so pretty dark. Before this I thought it was impossible to refinish veneer. It was only the inner panels - I don't think I would have attempted an entire piece of veneer furniture.

If you want to try stripping use a gentle citrus stripper and very light sanding. Test in an inconspicuous area first if possible since some veneers are thinner than others. Since you are going darker you can try using the gel stain method over older finish - see tutorials online. There are also some who have used the Miniwax Polyshades which is a stain and poly in one and can be applied over an older finish with the right prep. I have not done either of these two methods but there is a lot of info online.

I did apply a new finish over an old finish on a door with veneer on the stiles and rails that was losing its finish from bathroom steam. It was a very minimal veneer. I lightly sanded as much of the loose finish off and then applied a new finish and it went well.

I am a petit woman without much muscle, so when I sand, it is always lightly:) I admit to using my palm sander on the cabinets and on the door with 150 used sandpaper. Both were in such bad shape I did not think I had anything to lose and my arthritis was getting to me - otherwise, I would never recommend a palm sander on a veneer.

the only indication i have that the finish is gone is the fact that it is very dry feeling and it has zero shine. does that not sound like no finish? it stood in the window of a store for a lot of years. how did the walnut come out? Many, many moons ago, I wanted walnut, cause I really like dark, but the grain showed a lot, it just did not look right. I painted my floors black about 4 years ago and that came out a lot better?

I LOVE gel stain. Look into it, it may be the answer to your problems.

Actually - now that I think about it, I am not sure if teak is usually finished as more common woods are. I think it might be more frequently oiled with teak oil. It probably can be stained darker, but that might depend on what if anything is already there. Do some online research. Maybe one of the guys who works with teak will respond here. If there is a door or drawer that you can take to a reputable paint store or woodworker, they might be able to tell you what you have and how to proceed.