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See what 3m themselves have
http://www.3mdirect.co.uk/industrial/double-sided-tapes/3m-vhb-tapes.html -
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?
http://www.amazon.co.uk/dp/B016LCTY66/
3M VHB is great stuff, but make sure you get it right first time!