I am using XFCE, and here "reversing mouse buttons" act is completely independent of cursor theme. I guess GNOME and MATE behave the same in this regard.
Regarding presence of left-handed cursors in Adwaita theme -- actually I investigated this, and no, there is no left-handed version of it, it just contains the left arrow for special actions in GUI, but the whole theme is still right-handed. If there were left-handed version of Adwaita I would probably just use it. But the fact is that in repo there is only "comixcursors-lefthanded" left-handed theme available, and this one is a bit, ahmmm, blurry.
Thanks for advice on how to do forking, I will try to go this way.
BRs,
Denis.