Hvidt dresser help / dimensions needed  

Glad you have the one with legs. So much better than the plinth bases.
Perhaps you've already seen this, but this seller has photos that would seem to let you infer most of the information you would need:
https://www.1stdibs.com/furniture/storage-case-pieces/commodes-chests-of...

I bet tchp can help you out with more detailed information.

I can look at one this weekend that is at a local shop, and measure the mirror frame and take some photos.

I would be very grateful.

Another image

Here are some photos with measurements. The first image shows how the mirror frame disassembles, via three brass screws on the bottom section of the frame. The screws appear to go into the back panel of the mirror's frame, as the screws are set back to the back edge of the wood frame.
Other images just show dimensions. The mirror frame's outer dimensions are 37cm wide x 38cm tall.

Another

Another

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I have some dimensions of the stained beech part that the mirror hinges off of, which slides in the track. I was unclear whether or not you have that piece or not.

Forgot to add this dimension earlier

OMG, thank you so much! I do still have the sliding mount piece.

Sorry I forgot to measure how far the inset of the mirror glass is into the frame. It looked like 1/8" to 3/16" from the glass to the face of the frame. I will try to measure it the next time I am back there. The mirror frame has no particular profile, and the wood is all square edged stock that has been hand sanded to provide a pretty soft radius to the edges. The hand sanding is the only shaping that was done.

By the way, it is not too hard to get teak these days from Costa Rica, but note that it is a low, run of the mill grade. You can probably trim a sufficient amount of quality stock out of most pieces as long as you avoid the sapwood. Knots, too, but they aren't so much of a problem in teak. Fortunately you need very little teak for this mirror. And it is generally possible to find vintage veneer on ebay as well.
There will probably be a color mismatch between the dresser and the mirror frame, but you can probably remedy that with a bit of custom tint added to the oil.