No, that would presume (with no reason to presume it) that the information was conveyed to him in the OR and not before.
Let's go back to what I said:
For Shaw to have been right, the bullet could not have come out at any point before he left the OR. This statement is completely agnostic as to when Shaw became aware of the thigh wound and the possibility of a bullet therein, at least so long as he knew before he left the OR after the chest procedure. Of course, if you think differently, you could always provide your reasoning, rather than belching out unsupported assertion after unsupported assertion.
That’s because you also presuming (with no reason to presume it) that there was either a bullet in Connally’s leg the entire time or there was never a bullet in Connally’s leg the entire time. It doesn’t consider the possibility that both Shaw’s statement and Gregory’s statement could be correct, but at different times.
What evidence is there that the bullet came out or was removed at any time during Connally's presence in the OR? Nothing. So any scenario you might be dreaming of here requires a whole slew of assumptions to explain what happened, whodunnit, and why we don't know about it. in short, FAIL.
A few things you might want to consider:
Gregory arrived in the OR not long after Shaw. Shires arrived in the OR when "the chest wound had been debrided and was being closed [...] and the arm and leg wounds were being prepared for surgery. There are no gaps between Shaw's, Gregory's and Shires' presences.
Operating rooms are, by sanitational necessity, austere spaces. It's not hard to spot a foreign object that's fallen onto the table or onto the floor. They are also, by the same necessity, cleaned often and thoroughly. The only place in the OR where you might expect to lose something is in the patient's body. The chances that a bullet would roll around on the floor undetected is close enough to nil to be discounted unless evidence of this comes to light. And that evidence is also nil.
In his book Unnatural Death, Michael Baden says that, once they're all the way in, bullets do not fall out. As the bullet penetrates through the soft tissues, the tissue stretches before failing. The result is that the permanent wound cavity is slightly smaller than the object that made it. So when everything comes to rest, the wound track closes behind the projectile, holding the object inside. I've read that there are cases where a bullet that lodged near the surface was worked outwards by the cumulative effects of body movement to a point where it can penetrate the skin and be removed by hand. However, this takes months or years after the initial injury, so that doesn't apply here. The idea that Connally's thigh wound went from hole with a bullet hidden inside to Free Willy without human intervention is also vanishingly small.
MT: I'm only making one assumption, and it's used only as an explanation to reconcile Shaw's statement with the other evidence. Whatever extra assumptions you assume I'm assuming are your own assumptions, not mine
No, they are yours. You’re making a whole bunch of assumptions about what must be true if Shaw’s statement was ever correct. Assumptions specifically designed to promote your version of events.
If you want to assert that Connally still had a bullet in him when he entered the OR, but became mysteriously bullet-free when Gregory took over, then you need to explain how that happened, when it happened, who made it happen, and (hopefully, though not necessarily required) why it happened. If you lack evidence to answer any of these questions, then assumptions must be substituted instead of evidence. And there isn't any evidence that it went down this way. You're left with assumption stacked upon assumption all the way down, like turtles. I'm just reminding you of this. And you don't like it one bit.