This would have been a slightly tougher matchup for Hillary than Lazio, but the toughest opponent in 2000 for her probably was Pataki and he didn't run.
Hillary Clinton (D,WFP) 48%
Rudy Giuliani (R) 44%
Joe Dioguardi (C) 7.6%
Yeah, if Giuliani runs & no scandals come out, then him losing the Senate race by ~4 points sounds about right. Hillary's reputation would presumably be somewhat enhanced thereafter as a result of having defeated a high-profile opponent, so the more interesting butterfly that could end up happening as a result of a Giuliani Senate campaign would be Hillary winning the Democratic nomination in 2008.