How much does the overtone series dictate the timbre of sounds?

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I’m a musician and understand that a trumpet and violin playing the same note sound different because of “timbre.” I also know that a defining characteristic of an instrument’s timbre are the harmonics involved. But if I somehow manipulated (in a spectral analysis or something) the overtones of a trumpet to EXACTLY match a violin, would it sound EXACTLY like the violin example? Or are aspects such as the difference in material shaping timbre in ways completely removed from harmonics?

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Yes, if you edited the overtone series to be identical, the trumpet would sound like a violin. This is because the sound waves are produced by simply adding all the overtones together, so the sound waves would be the same. It would be a very impractical way to make a violin sound though, and you probably wouldn’t be able to get it close enough.