> take scissors to a sheet not an option?

My experience is that it is quite difficult to cut the sheet precisely enough if you just use a normal pair of scissors.

My technique was always 1) fold along the line you want to cut (makes it straight—maybe parallel if you have a good eye), 2) use your tongue to wet the creased edge, 3) open and re-fold along the same crease but for the opposite side (valley becomes mountain fold), 4) wet the creased edge again… It was easy enough to tear along the fold at that point.