Ok I feel like we are talking about two distinct things that are being interchanged freely when they cannot be. There are two types of motion relevant here but first the assumptions; our model skier is making a single edge-locked, park and ride carve from the top of the turn until he's facing uphill and gravity stops him. His technique and fitness is perfect such that he is always able to keep his balance at precisely the center of the ski, thus load is evenly distributed along the length of the ski. The surface is also perfectly firm and even.
Circular motion: rotation of a body around a fixed axis outside of the body's COM. This is the arc of the ski with some radius X, the axis of the turn being located at the center of that radius. This motion is what gets our model skier from facing left to facing right relative to the fall line. All that is required for this motion to occur is centripetal force generated by the ski on edge, assuming the skier has some speed already. However, we still do have torque (force times distance) in this system from the force of gravity acting through the skier's COM at rN distance from the rotational axis as poorly illustrated by myself in the image below. Hence why we accelerate both in linear velocity as well as angular velocity ω as we pass through the fall line but decelerate in both as we continue a turn past 90deg to the fall line and uphill.
View attachment 190147
Now, a ski being tipped further on edge results in more centripetal force at a smaller radius. This increase in force explains the linear velocity change we observe with the ski in circular motion undergoing a radius tightening, as you note though there is also a corresponding increase in angular velocity ω (rate of rotation about the
axis of the turn). A change in ω requires torque this is true. As mentioned previously, we already have this torque as a consequence of the constant force of gravity on the skier COM at varying radii from the axis of rotation while in circular motion. Side note, from this you can also sort of intuit that there's a maximum rate of increase for ω and therefore centripetal force, meaning that if edge angles are built too quickly the amount of centripetal force able to be created to hold the skier up in the turn can be exceeded and you fall inside, something most of us have experienced at some point.
Rotational motion: rotation of a body about an axis passing through its COM. This is almost assuredly not happening to our skier. Remember load is evenly distributed along the length of a ski in a carve and this will resolve directly under the skier's COM. Gravity is acting directly through the skier's COM. There is a frictional force along the base of the ski that theoretically represents a moment about the COM but this is easily overcome by gravity in a turn and our bodies can generate sufficient internal forces so as to prevent our legs from moving separately from our upperbody/COM. To be clear this, force balance absolutely goes out the window when skidding is introduced and the ski is asymmetrically loaded.
This difference is why I think the torque Franko was talking about it is in reference to the ski itself bending, nothing to do with changes in angular velocity, ASSUMING he's talking about a carving ski not parallel or short turns. The ski itself is not generating any asymmetric torque on the skier to influence angular motion in either regime of motion.
Given all the above, I'm confused by what you're saying here. What mass is rotating about the COM? Are you talking about the skis/feet moving separately from the COM/upper body? For short/parallel turns I would agree with you certainly then that there is rotational motion occurring from the tips being loaded more initially which rotates the feet/skis about the COM causing the turn to occur much faster/sharper than is possible via centripetal force and gravity. The skier then naturally uses the tails a bit to arrest the rotation enough to begin the next turn.
This all is of course very grey in the real world where skidding/edging is blended, imperfect technique, the skier manipulating the motion of their COM through muscular effort instead of passively accepting forces, snow conditions etc.