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Ferret, really I don't think you're far from being able to read fingerings from sheet music.
Once you know the key signature, there is exactly one letter (be it flat, sharp, or natural) per line or space on the staff,
You find the key sig at the beginning of the music, then find the matching fingerboard diagram. Then you just match up the lines and spaces with the letters ... if it's a simple piece, meaning that it doesn't have any accidentals (flat, sharp, or natural signs outside the key sig).
And for the most part, it's also just one letter per finger. Therefore the fingers usually match up simply with the lines and spaces, one finger per line or space.