Hmmm it really does depend on (A) why Dole isn't running ITTL and (B) when he makes it known that he won't be a candidate. He was seen by most 'republican establishment' types as the obvious 'air-apparent', so the reasoning behind his non-candidacy is important.
If he makes his intentions clear relatively early on, I can see this potentially encouraging a lot of people who sat out the 96 primaries to enter the race. I think Cheney, in particular, entertained the idea of a run in 96, though he decided against it. I can see Jack Kemp ending up as the 96 nominee in this scenario though. If that's the case, he'd probably fair better than Dole did historically, though he'd still lose barring other PODs. My guess is that he'd probably do about as well as Romney did in 2012 against Obama, electorily speaking anyway.
If Dole's decision is more last-minute, I could still see Kemp possibly entering and winning, though if it's too late for that, someone like Alexander would probably end up winning the nomination and ultimately losing to Clinton in a similar fassion to Dole in OTL.