I haven't done CTS at multiple corner but I would assume its due to skew variation as you mentioned. Skew can vary across corners because metals and transistors scale differently. ex. from bcs to wcs corner your net delays may scale by 3x while your cell delays scale by 2.5x ( i made these numbers up as an example) This means clock paths that are metal dominated vs. clock paths that are cell dominated will have different skews depending what corner you are at