I personally think that the Composite Human could very likely devise a strategy to knock out the Plague Doctor without being touched, they are much stronger physically and unfathomably skilled so it shouldn't be a hard task to pull off.
I'd imagine the situation turning into something like this:
"His mind was wandering again. What was he doing? Ah, yes.
With long, well-trained fingers he began digging into his abdomen. The flesh there was yielding, properly porous, neatly organized. Now, where did he leave his bone saw? Oh yes, the liver cavity. Reach about over there and… ah, there it was. Hrm, the thing was getting dull, and he had no idea where he was going to get a new one. Never mind that for now, he reminded himself. Next, the scalpels. The long ones were stashed within the bones of his pelvis, and he had a devil of a time getting them out of there. He really needed to find a better place for them, but his body only had so much room, and any size-increasing modification were bound to be too easily noticed in his current surrounding. Perhaps a second cranial compartment? Something to consider after he was finished with this procedure.
He was forgetting something, he was certain of that. But what was it?
He dug out his dwindling supply of adhesives from within his left eye socket. This required the temporary removal of the eye, which did not make the task any easier. Still, when it was done, he had all he required to continue. Spreading his robe more evenly on his body and positioning the hem of it to support his neck, he began the operation proper.
This one was going to be difficult. In order to reach that part of his brain that he wished to remove today, he'd have to bypass some rather essential segments. Failure to do so may result in severe harm to his memory, which would obviously be catastrophic, considering he had no access to his old fallback brain anymore. Not that he would switch to that one anyway- he had modified this new one over a period of at least three decades, and he was not about to let all that work go to waste. No, he would simply need to be very careful, and that was all there was to it."
I feel as if CH’s only real chance is to shoot SCP-049 so many times he literally doesn’t have legs anymore.
This, admittedly, may take a pretty long time, since SCP-049 is pretty resilient to bullets.
It does help that SCP-049 walks everywhere and isn’t great at sprinting.
The zombies die with little issue, CH is a good enough shot to deal with them. Hell, CH could incap SCP-049 via... talking to him.
SCP-049 is extremely neutral to scientists, and very rarely strikes against them. Given that CH is the greatest scientist to ever live, chances are SCP-049 would express great interest in CH and not attempt to kill him.
So, I guess CH would win via talking 049 down with science talk?