There is absolutely NOTHING "unusual" about his hat - except possibly that it's civilian rather than military, and there's certainly nothing unusual about that either. A close-up look at any crowd scenes like those @JPK Huson 1863 often provides us with will reveal plenty of them, especially in urban settings like Washington, D.C. or New York City.
I'll add that unlike the group photo of Mosby's Raiders above I believe the subject in the OP is the "real deal" - that is, a genuine wartime image. I've seen the flared bell crown in photos and prints from the 1850's and ca. 1860 but think that by the end of the war that feature had become passé, as the group photo seems to demonstrate.