I like to use tiny hexagons which I do not reuse. Instead of tacking corners, I baste the edges I fold over going through the paper. I make a big knot at the end high contrasting color quilting thread or double strand regular thread and baste around the edges leaving a tail hanging. I leave the papers in as long as possible to add some stability while I work. After they are sewn together in my pattern, the big knot helps with gripping the thread for pulling.
i also cut hexes with a die machine but I have not found a die for the smallest shapes.
I use recycled paper from junk mail, thick non-glossy pages in magazines and card stock scraps and I use a hole punch to punch a hole in the hexes. This makes removal of the hexes easy by using a chopstick (or any blunt object that fits in the hole) to lever it out.