I think the reason for describing the lateral force from the wind as a force along the altered axis of the bullet is 1) emphasises that the bullets axis does quickly change to align into the wind (also perturbing its' flight with "aerodymanic jump") and 2) to make it clear the airflow will be parallel to the bullets axis so the force on the bullet is from its nose, not the side. This means that the wind deflection depends on the ballistic coefficient, not its profile area, length etc. Litz explains this in his Applied Ballistics but its really best not to try to read it at bedtime in my experience.
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