Well for Wilson, Charles Evans Hughes one of America’s greatest lawyers was the Republican nominee in 1916. Hughes had gone toe to toe with some of the worst robber barons on Wall Street and served on the Supreme Court so he would have certainly done a better job representing America’s interests at Versailles than Wilson. Also the Republican Senate would have been obligated to approve any treaty Hughes brought back. Voters however thought Hughes was for war and Wilson for peace.
As for Madison, almost anybody. Had he simply ignored the war mongers something that is tough in any age. He could have avoided the war and got the same thing.
The problem with resumes is they often fail to reveal character or leadership traits.