Watergate isn't some unavoidable event. The factors leading up to it and like behavior was unique to the circumstances Nixon and more importantly his staff were facing OTL. Without a dragging Vietnam it wouldn't have occurred. Without the Pentagon Papers, it wouldn't have occurred, Without Haldeman and Erlichman it wouldn't have occurred.
Vietnam and the stress it put on Nixon played heavy roles into the atmosphere surrounding the lead-up to Watergate. But it was the Pentagon Papers that triggered the paranoia. Which, in many ways was rightfully placed to some degree. Those reports heavily threatened (at least appeared to) Nixon's secret negotiations and diplomatic chess to strengthen ties with China, ease tensions with Russia, and bring Vietnam to the table. He however, vastly over-corrected.
If Nixon came to office in a scenario were Kennedy makes it long enough to change and leave an impact on Vietnam policy, I heavily doubt anything resembling Watergate would occur.