Easy. The bullet was there when Shaw spoke (he didn’t say where he got the information, but he didn’t say he just assumed it), and then either fell out or was removed before the surgery.
We have Connally’s report of a bullet falling on the floor and we also have Wade saying in an interview that a nurse showed him a bullet that he told her to give to a policeman, and Bobby Nolan saying that he was handed an envelope that he was told by a nurse had a bullet in it.
The bit from Connally's book doesn't work in this scenario. There is the previously mentioned admission by Connally that he's not really the most reliable narrator on this. But there's something more. He said that the bullet fell out wen he was being moved from a gurney to "the examining table." "Examining table" implies Trauma Room 2, rather than the OR, which would have an operating table. The bullet didn't even make it out of the ER, and was therefore unavailable to be in Connally's thigh in the OR.
Even if we assume (Iacoletti.assumptions++) that Connally really meant "operating table," there's still a problem. If you read the nurses' and surgeons' testimony, Connally's gurney was never actually wheeled into the operating room. Instead, the Operating table was brought out of the OR and Connally was moved onto it before being whisked into the OR. So the bullet would still have never made it into the OR, and would have fallen out well before sawbones Shaw ever sawed the Governor bones. Shaw is still wrong here, no matter how you cut it.
And you bring up Robert Harris' beloved wandering-nurse-with-a-bullet. As you note, Henry Wade said a nurse came to him with what he said was a bullet while he was in the waiting room with the Connally party. And Trooper Nolan, another member of the Connally party in the waiting room, was given an envelope by a nurse who told him it contained a bullet. Nolan himself said he didn't know whether it really was a bullet or not. Bill Stinson, Connally's aide who actually insisted on being in the OR while the surgery was going on, was talking with Nolan at the time and remembered it about the same was as Nolan. And I will admit that this is something of a mystery as to what actually occurred. Complicating matters is that there is a small envelope in evidence that is filled out in Audrey Bell's handwriting and has Nolan's initials in his handwriting. Both Bell and Nolan authenticated their own writing on the envelope. The problem is that this envelope contained "bullet fragment," as stated in Bell's writing. Bell herself says it contained small fragments she retrieved from the scrub nurse at the end of Connally's surgery, and not a bullet. In fact, it's the CE842 envelope.
To shoehorn the wandering nurse into our debate, you need to assume some large combination of:
1.) Bell was lying or Nolan was visited by a second nurse (he only ever mentioned one)
2.) that said bullet was retrieved from Connally's thigh, and not from some other source after Shaw left the OR
3.) that Gregory and/or Shaw were lying and the x-rays were forged
4.) that this happed with out Stinson noticing, or maybe Stinson was in on it.
5.) that the other OR personnel (ie, scrub nurses, circulating nurses, assistant surgeons) either didn't notice or were part of the coverup.
Those are a lot assumptions that have to be added for Robert Harris' patented wandering nurse theory to be correct. My explanation is simpler and requires much less assumption.