Rudy would pick the judges. At best Ted Olsen may have some influence over the nominees, but the judges are not picked by advisers, they are picked by the President.
I suspect that every one of Rudy Guiliani's appointments will have the same liberal social views as Rudy Giuliani. If he did nominate anyone closely resembling Antonin Scalia, do you think Rudy would fight to bring his nomination to the floor or would he apply any pressure on the Senators to confirm him or her? Not bloody likely.
Remember David Souter!
John Sununu picked David Souter.