Sorry for the delay on this. I was out of town when you asked originally.

Tenskwatawa's account of day-to-day Shawnee affairs is generally considered reliable. It's version of Shawnee oral traditions has been questioned (such as in The Middle Ground by Richard White, which would be looking into as well if you're working on something involving indigenous Ohioans, though I didn't include it on my original list of suggestions for you). White was mainly criticizing another Trowbrdinge-Tenkswatawa collaboration, but his points can be applied to Shawnese Traditions as well. Mainly, he feels that Tenskwatawa's telling of oral traditions are tweaked in such a way as to make them allegories for the lives of himself and his brother Tecumseh. There's also some issues with Tenskwatawa's oral traditions not lining up with Black Hoof's, but I'd be less concerned with that. Tenskwatawa and Black Hoof come from different subdivisions of the Shawnee, and seem to be telling similar stories from the points of view of those subdivisions. Some unique aspects of Tenskwatawa's oral traditions, such as the arrival of the Shawnee from across the "sea" are also mentioned by other, earlier, sources, even if Black Hoof doesn't mention this. There's been some question over whether the "sea" in question is actually the Great Lakes, a mythic invention of some sort, or an actual reference to the ocean (In Iroquoian Women, Barbara Alice Mann interprets this portion of the Shawnee origin legend as a reference to Taino refugees fleeing Caribbean for mainland North America sometime after the Spanish arrival in the New World and intermingling with the Shawnee while they were in Georgia). As for his opinions on Euroamerican settlers, he's rather mellowed out in Shawnese Traditions, but his stance was on the issue was dymanic. I discussed that a bit in this post (also has a few other sources you might be interested in).

You'll want to keep an eye on Trowbridge too. He's not bad by any stretch, but Shawnese Traditions and Meearmeear Traditions were both commissioned by the Lewis Cass, one of the main architects of the Indian Removal policy that would be implemented a few years later. It's good to be aware of the era in which these were written.