Wade Hampton, commanding the cavalry corps of the ANV. Also Richard Taylor in the Trans-Mississippi.
There were more untrained/non-West Point men commanding corps in the Union Army but I´m not sure about their records (Dodge etc). Also alternative military education like prior wars (Fremont, Hurlbut) or militia service (Sickles, Butler, Cox). And some with foreign experience like Osterhaus (solid but somewhat unspectacular) and Sigel (rather opposite).