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I saw a tip on a youtube diy channel about how to cut thin strips of tape that might help?
Find a sheet of glass (if you can), clean it thoroughly to avoid buggering the tape adhesive, lay a strip of tape along the edge overhanging by the width you actually need and then use a sharp stanley knife to cut along the edge of the glass. Gives you a nice, clean, straight edge.
They did it to make narrower strips of masking tape for intricate designs. The idea might be transferable?
That's what I was thinking and then just cutting a 3mm strip off.
It's just that it's a pain to cut strips that small and I assumed that this stuff would exist if the laptop has a full run on both sides of the digitizer :(