I also received a caning like this from Goddess Hayden in the mid-2000s in NYC. I think she retired a long time ago. I've seen videos of Cybil Troy give a hard caning without causing any marks.

I may be remembering inaccurately but someone explained it to me once: Apparently the cane needs to be brought straight back up from the point of contact with the body without any lateral motion. Apparently it's the lateral motion (dragging) that causes the welts. It also needs to be brought straight back up using a rapid flick in the wrist so that the tissue, nerves and blood vessels can rapidly uncompress.

I can't verify that this is true. I'm a switch, but I've never really learned how to use a cane properly. This also may simply be a lost art in which case I just have to accept that I'll never be on the receiving end of a caning again.