You can't prove a negative, but we're as sure the answer is NO as it is possible to be.

We know this didn't happen because before the 20th century, presidents didn't campaign in the way they do today. In the early years of the Republic, it was considered gauche to go out and solicit votes. Before 1800, it was expected that a candidate's friends and neighbors would nominate him to office because of his known wisdom and skill, and that these known quantities would be obvious enough to abrogate the need to campaign.

Democratic ideals began to infect the political process as soon as Washington's second term, however, with some in Congress -- particularly in the House -- beginning to campaign for themselves. This attitude was slow to reach the presidential election process, however. When Aaron Burr attempted to do so, he was largely ridiculed. It wasn't until the 1840 presidential election and the election of William Henry Harrison that you start to see relationships to the campaigns of today.

There are limits to that relationship, however. In 1860, for example, when Lincoln ran for office, he performed only one campaign appearance, and that in his home town of Springfield, Illinois, where he offered a few short words. Candidates were supposed to stay out of the limelight and let proxies do the dirty work of fundraising, speechmaking and arm-twisting necessary to get a candidate elected. It was considered unseemly for a candidate to go out and do that kind of thing themselves.

And yet, desperate candidates started doing it anyway at the time of Lincoln. As I wrote in a previous answer about Lincoln's campaign finances, Democratic candidate Stephen Douglas broke new ground by deciding campaigning on his own behalf. He didn't have the money Lincoln's campaign had, so hit the road and hoped his stage presence would carry the day.

Republicans in New England responded by posting a series of handbills seeking help for "A Boy Lost!" The handbills described the lost boy as "about five feet nothing in height and answers the same in diameter the other way. Has an idea that he is a candidate for President."

Subsequent candidates would take to the campaign stage themselves, following the example of Douglas rather than Lincoln, but I've never seen the slightest iota of evidence that a body double was ever used. It would be ludicrously simple to detect, and any candidate would instantly lose the election by pulling such a ridiculous stunt.

Even in Lincoln's election, news and information was carried instantly across the country by telegraph, and it would be an easy task to realize that someone couldn't be speaking in two places at the same time. Presidential candidates, even in the 19th century, were known people. Broadsheets carried their faces and names, and they were constantly surrounded by hangers-on, staff and those who wanted to be both.

The notion of a body double only works in societies without a free press and where information is restricted. Even in the earliest years of the United States, that wasn't the case.

Not a presidential campaign, but related to the question -

(I first heard this from Robert Caro's biography of Lyndon Johnson.)

When Johnson was running for Senate in 1948, he campaigned around Texas in a helicopter. He wouldn't have time to stop in the very small towns, but the helicopter would hover over the town and he would give a little speech. But the people couldn't really see who was talking. So sometimes, when Johnson wanted to take a nap on the campaign trail, the helicopter pilot would give a little speech instead, saying that we was Johnson.

From http://www.lbjlibrary.org/press/lbj-in-the-news/campaign-by-helicopter :

Between the scheduled stops, Johnson swooped down on highway crews, section gangs on the railroad, and farm workers. In the early days he took the mike and hailed them over the loudspeaker. He identified himself and asked for votes. After he realized that the rotor noise and raspy loudspeaker prevented listeners from knowing who was at the mike, he turned that job over to the pilot. Speaking in a Texas drawl, the pilot asked for votes and chucked handfuls of brochures (sometimes accidentally accompanied by a Thermos jug) out the door. Meanwhile, Johnson was able to nap between appearances.