Gently run a stanley knife across the end of the ribbon, about 5mm in from the end, do it firm enought to cut into the insulation, but not too firm that it cuts into the wire inside. (maybe practice on the BAD ribbon to get a 'feel' for it.).
This will create the 'starter cut' (weakening the plastic insulation).

Then, use small sidecutters and GENTLY close the blades of the cutters into the cut from the knife and pull the cutters away from the end, thus stripping of the 5mm plastic ends. (hope that made sense).
You need to focus more on pulling the cutters away, rather then closing them tight which would cut right thru the wire...it's an aquired skill, so practice practice practice.....


MM.