Shadow fang is applied every "full rotation" if you would call it that. So no matter how you do it, lets say dancing > shadow > mutilate > aeolian just for the hell of it, it will still be applied after every dancing edge as the timing is specifically setup to account for this rotation. It becomes every 9th action as you've stated above. Adding the huton refresh to the end of the shadow fang combo means that it would fall off before it could be reapplied in the instance of the huton buff because you are adding another action ontop of the others as opposed to replacing another.

By replacing it with aeolian there is zero risk of losing any dots and it allows the timers to keep alignment to what they are now. The dots are the highest potency weapon skill the ninja has. Even if the potency of the huton refresh weaponskill was to be 0 it would still be a net dps increase as the extra raiton would make up for it and then some (raiton potency > aeolian edge) and you would also be minimizing gcd clipping by removing a 3 input mudra from the general mudra roatation further negating the effect of mudra lag.

Theoretically speaking if the huton refresh weaponskill does apply huton for the same length you will be replacing every fourth aeolian edge with it. It will also allow you to use an attack mudra when you have < 20 seconds left on huton further allowing for more leniency in mudra use instead of as it is now being forced to refresh huton. The huton expiration would no longer effect your mudra use unless the extension move has some sort of diminishing returns.