We have discussed numerous alternatives to Spiro Agnew for Nixon's running mate in 1968 but not AFAIK Rogers Morton,
https://en.wikipedia.org/wiki/Rogers_Morton then Congressman from the Eastern Shore of Maryland, brother of Kentucky Senator Thruston Morton, and in OTL future Republican National Committee chairman and cabinet member (Secretary of the Interior, then Secretary of Commerce) under Nixon and Ford (and for a while the latter's campaign manger in 1976).
"At midmorning, back in his suite, Nixon assembled with staffers Mitchell, Haldeman, Ellsworth, Tower, Finch, and Rogers Morton. Nixon was disturbed by the lack of enthusiasm shown for Agnew and asked Finch if he would consider the vice presidency. 'Nixon was dead serious,' said Finch later, 'and I was equally serious in saying I wouldn't even think of it.' 'He was deeply moved by my suggestion,' recalled Nixon, 'but he strongly rejected it, arguing that the leap from lieutenant governor to Vice President would be perceived as too great.' Nixon next turned to Morton: 'Rog, maybe you would be the better choice for me.' But Morton insisted that he lacked the credentials. 'That pretty well clinched it for me,' recalled Nixon. 'Had Morton said that he wanted it, even at that late moment I might well have picked him.'..."
https://books.google.com/books?id=mj70AgAAQBAJ&pg=PA116 Nixon explained that "Politically he had the same border-state advantages as Agnew. I knew him far better than I knew Agnew, and I considered him one of the best campaigners, one of the ablest individuals, and one of the most astute politicians in the party."
https://books.google.com/books?id=UyfcLYY9F0gC&pg=RA1-PT347
So suppose Morton responds positively (instead of saying as in OTL "If you want to know the truth, if it's between me and Ted Agnew, Ted would be the stronger candidate") and is chosen. Presumably he becomes president on Nixon's resignation in 1974, since I don't see his being VP much changing the course of Watergate. What kind of president is he, will he run in 1976, if so will Reagan challenge him (and how successfully) etc? Note that if he wins the 1976 general election as well as the primary, he may die of cancer before his full term is over (unless the change in his political career butterflies his cancer away). As the Wikipedia article notes, "Morton had been diagnosed with prostate cancer in 1973, but he said that the disease was in its early phase and was still treatable. In 1979, however, Morton died of the cancer at his home in Easton."