I was advised to "size" the leather with PVA glue, layered in cling-film and set aside for 24 hours to dry, before attempting to cut and fit. This really does stabilise thin leather (mine was from a bookbinder), but it loses a lot of it's character.
If you can get thin double-sided adhesive (ask Greyhoundman) I would say that putting this on the leather before cutting would provide the same level of support, but would not stiffen the outer surface.
As suggested above, some form of pattern to work to would be a good idea - I cut mine from old wallpaper, then transferred the dimensions to the leather.