my wife and I were hiking in Northern Tennessee, Southern Kentucky. We found two of these running around. There were no tibial spurs. I was wondering if these are trapdoors, and if so, what species they are?

Yep, definitely adult male trapdoor spiders in the Genus Ummidia. The taxonomy of these guys is about as bad as Aphonopelma and there are literally dozens of undescribed species that we know about (and probably dozens more that we don't!)