In my experience, no glue is going to actually take the finish, but hide glue may be your best bet. Whatever the binder, I would try and make the patch the color of the finished piece. It would take trial and error on some scrap but that would be my method.
Also, if your dovetail gaps are not paper thin, I would cut wedges to fit the gaps, with the grain running in the proper direction they almost disappear. I have even enlarged gaps so that I could then fill them with a wedge and they look better than not trying that "scary" enlargement.
Good luck!