1st- Download Roger’s book from the wheelpro website, worth every penny.
A £5 Spokey (red) will be the first and only spoke key you will ever need. (unless your using far eastern or odd factory built spokes, but unlikely. They are superb, don’t be fooled by the price.
Practice lacing the wheel up with the spokes you have. You’ll get a feel for how long the spokes are you actually need. The spoke calculators are not as good as experience.
FFIW, I’m very suprised to hear that the new rim needs 3mm shorter spokes on only one side, are the eyelets offset on the new rim then?