Source:
Report of Brig. Gen. Jones M. Withers, C. S. Army, Commanding Second Division.

April 6-7, 1862..--Battle of Pittsburg Landing, or Shiloh, Tenn.
O.R.-- SERIES I--VOLUME X/1 [S# 10]
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"...under command of Brigadier-General Gladden, moved out of camp, marching in line of battle, and shortly after 7 o'clock came upon the enemy, when the engagement commenced. One of their batteries was playing upon us with effect, but in a short time Robertson's battery was brought on our side, which soon silenced theirs. We then charged, driving the enemy flying through their camp. In this charge several colors were captured.

Just before this charge was made General Gladden, while gloriously sustaining the reputation won in Mexico at the head of the immortal Palmetto Regiment, received a wound from a cannon-ball, which proved fatal..."

Source:
O.R.-- SERIES I--VOLUME X/1 [S# 10]
April 6-7, 1862..--Battle of Pittsburg Landing, or Shiloh, Tenn.
No. 192. -- Report of Col. Z. C. Deas, Twenty-second Alabama Infantry, commanding First Brigade.
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It appears he was wounded very early in the morning. More reason to believe the surgery was performed on April 6, 1862.

There is a book titled "Medical Histories of Confederate Generals" by Jack D. Welsh that is available free online using Googlebooks but Gen. Gladden's entry is simply a copy of what Ezra Warner wrote. I suggest talking to some of the writers and historians on here about how to present any conclusion you come to. Personally, I would have no problem if you said it is likely the surgery was done on the 6th but I'm only a reader of books, not a writer so my opinion is about worthless LOL!

Cany you tell me what your interest in Gen. Gladden is? Ancestor, research project etc?