In Edward Behr's (excellent) 1996 book Prohibition, he gives a precis of early American drinking habits in the opening chapters. He quotes contemporary accounts that speak of whiskey flavored with apples, cherries and mint (as separate drinks).
While it is hard always to see what is meant - e.g., whiskey flavored with apples might have been applejack, and the whiskey flavored with cherries, cherry bounce - whiskey flavored with mint would have been whiskey with mint leaves added for a bouquet, sweetened or not, as the drinker preferred.
We must recall too that when the early mint juleps were devised, the whiskey would have been quite young and probably needed a touch of sweetness. Today, well-aged bourbons are often reasonably sweet from the wood sugars. E.g., a julep made with Rock Hill Farms, or Weller 12, wouldn't need any sugar arguably, or less than might have been used in a julep 200 years ago.
A mint julep made from a whiskey such as Mellow Corn, or Jim Beam Rye, or even white dog, might approximate more closely to the original mint juleps than anything normally drunk today under that moniker - not that latter-day juleps are bad (in fact they might be regarded as super-luxury versions). That white rye whiskey from West Virginia is another candidate, as are any of the whiskeys from Tuthilltown distillery in New York.