I wouldn't want that (but then I have pet peeves against using legendaries and shinies competitively, so I'm biased).
Customized legendaries and at-will shininess, much less both at once, should not be available in-game. They're supposed to be special because they're so rare, and some legendaries are intended to not be shiny at all.
Also, the Stat Judge's answers are in-character indicators of out-of-character information, so using him as an in-game editing program doesn't make sense. Editing Pokemon is what simulators are for, anyway.