Probably wrong regiment. General problem caused by higher headquarters. I found William in Hardiman's Regiment, Company D, 1st Regt Arizona Brigade, enlisted 15 October 1862 at Weatherford, TX. There are several Wheeler's in the Arizona Brigade. Look in the 4th regiment, several J's.
In the 31st TX Cavalry Regiment (Hawpes) there is only Charles P. Wheeler.

I basically used the National parks service soldiers lookup and regiment look up. Then went to Footnote.com for detail. In the soldier look up put in Wheeler, TX, Cavalry, Confederate to get a list of wheelers by regiment.
The regiments of the Arizona had several names. Hardimans, Silbes and numbers 1st through 4th, AZ Arizona Brigade.

Hope this helps