I believe the Scots-Irish and Scots played a predominant, and what might be called didactic, role in whiskey distilling in America in general, not just in Kentucky. This is why e.g., George Washington brought in a Scot to distill at his estate. Scots-Irish and (in particular, Lowlands) Scots people are, from this and many other standpoints, much the same thing. See the well-known study Albion's Seed, by a professor called Fischer from Brandeis University, on the close cultural and historical connections of these groups. E.g., the author points out the Protestant, Anglo-Saxon-derived Ulstermen almost never interrmarried with the Catholic (Celtic) Irish. He explains that trading and population movements between Ulster and the Lowlands in Scotland and far north (Borders) of England were numberless and ceaseless. Some southern Irish did clearly participate in Kentucky distilling - which is different from influencing its main form - but that came later. While there was some immigration from southern Ireland to America in the 1700's most of it did not start until the later 1800's. A good example I believe is the first Cummins who distilled around Bardstown, probably also McBrayer. If these gentlemen in fact hailed from what is now Northern Ireland, there can be no question a number of Irish from what is now the Republic came to America and some to Kentucky and some to distill but this was not before the mid-1800's, generally.
Unquestionably, they and other groups contributed to what bourbon and rye are today in America but I believe the predominant cultural influence which created whiskey there (as in Canada by the way) was Scots-Irish and Lowlands Scots. Some Highlanders, culturally different from the latter but distillers by tradition as well, may have added their shadings to the American distilling picture. There are I know a couple or more colonies of ex-Highlanders in North Carolina; it would be interesting to plumb their distilling traditions if any.
Good point, Mike, about the Lincoln County Process. I did not think consciously of it but it is in line with my idea about charred barrel aging since one is a version of the other. Jack Daniel had Scots-Irish roots, so did Dan Call his mentor. The Scots-Irish background here and its import in whiskey distilling is mentioned in a recent biography of Jack Daniels, I need to find its title but we have discussed this book here before. Not all Tennessee distillers were from this background, but what was the ethnic composition (predominantly) of Tennessee when the process started? Albion's Seed gives statistics and as I recall concludes the Scots-Irish were predominant. (I'll check it, there are also, by the way, a number of references to whiskey in this book).
There would have been no reason to use hardwood to prepare smoked malt in America because barley was used in a much smaller amount in American whiskey than Scots'. And, once you have some barley, the corn and rye and wheat can be used unmalted. Maybe they did try to use smoked barley malt to prepare the 10-15% of the mash that was (and is) barley but found the smoke taste too weak. I think barley would have been preferred as the grain for whisky in America as in Scotland and Ulster but corn and rye were cheaper to produce and more available and so were substituted early on for barley (or "bere", a more primitive form of barley used at the time in Scotland and probably Ulster. A Scots distillery has just recreated a bere whisky, as a historical experiment).
Another thought: we often speak of ethnic influence in this area as meaning that the ethnicity itself had to distill. Yes and no. Yes for the farmer-distillers because originally they distilled for themselves. Their taste for the product, which is culturally driven, would have spurred that process. Some farmers probably distilled just to make money, but most I think would have used the product. Later certain groups were by dint of their social and cultural history more likely to sample whiskey than others. To provide for this demand, both members of that group and non-members might enter the distilling trade. It became a trade early. M'Harry's book, written not longer after the turn of the 18th century, is addressed to the small businessman, the small-scale craft producer (there was no other then!). Of course, Americans, issuing from all kinds of sources, bought his product. But whiskey became the main domestic spirit as the 1800's wore on and I believe what kept it going was not the city trade who wanted expensive aged whiskey (which was only one form of whiskey) but the traditional rural- and frontier-based market which used common whiskey or bourbon aged a year or two at most (and we know the "red cretuur" can take good color even after only a few months in cask). Those areas of America were opened up mainly (i.e., in majority as I understand Albion's Seed) by the Scots-Irish and allied groups. The allied groups were the culturally connected Scottish Lowlanders and the Borders people in England. At the time in these latter areas in Britain distilling was legion.
In Cincinnati, say, with its early-implanted strong German and Polish populations (the Polish festival is starting soon in Cinnci by the way), beer was always a staple. In consequence, there were many producers (of whatever ethnic background) who catered to this demand. Those communities and some non-members around them became devotees of this drink and the same occurred in Milwaukee, St. Louis and other places. Whiskey did not become their main drink, it didn't have the cultural background and associations it did in the areas of America opened up by the Scots-Irish and allied groups. The reverse is true, of whiskey (IMO).