^^-- The continuing to arc over is close to if it came straight off a launch rod at that angle, it's not additional weathercocking. That's most true though with a lightweight rocket, a flying motor would have a lot more angular momentum, but that's not weathercocking either at that point. Problem is the wind sets off all kinds off problems and I find it unlikely the OP can beat a record if his launch conditions are substantially worse than those of the existing record.
I've seen a case, and had video, where a slow rocket could not only be seen angling into the wind, but additionally pushed sideways by the wind as soon as it came off the rod. By shortly after launch, regardless of how much weathercocking occurred, the entire rocket is moving mostly sideways with the air as a unit in addition to moving through that air. The only way weathercocking happens after that point is if the wind increases OR decreases (or changes direction, more complex same thing). If the wind decreases, the relative wind direction change to the rocket will be opposite of the original wind direction. It would take a complete wind halt or reversal to cause a very noticeable effect, but easily could be substantial compared to the what remains later in the flight of the original angular momentum, rendering that insignificant.