The short answer is in Matthew 26:24:That still leaves me wondering whether there isn't something theologically problematic about seeing those who do great evil as the agency of divine providence. Are there not other, better ways?The Son of Man goeth, as it is written of Him, but woe to the man by whom the Son of Man is betrayed. It had been good for that man if he had not been born.St John Chrysostom's comment is:But some one will say, Yet if it was written that He was to suffer these things, wherefore is Judas blamed, for he did the things that were written? But not with this intent, but from wickedness. For if thou inquire not concerning the motive, thou wilt deliver even the devil from the charges against him. But these things are not, they are not so. For both the one and the other are deserving of countless punishments, although the world was saved. For neither did the treason of Judas work out salvation for us, but the wisdom of Christ, and the good contrivance of His fair skill, using the wickednesses of others for our advantage.In short Christ showed himself as wise as a serpent and as innocent as a dove. But to answer your question, the tormentors were/are not instruments in the sense that a drill or saw is an instrument - they retain agency and hence guilt. As to the question what He would have done if Judas had chosen differently, I'm still working on it. Current working hypothesis: I think He would have found some other way (though the broad contours of the historical events would have been similar) - human wickedness not being a rare commodity - and that it didn't have to be Judas and no one else.