I agree with other responses indicating the papers should be left in until the heck is completely surrounded by other hexis. I also second the suggestion about the Fiskars hexi punch. It makes the cutting process easy!
I am working on a hand sewn hexi American flag quilt now. It will have @3000 1" finished hexis when I am done (I have @1000 sewn together so far) and I am amazed at how much the hexis keep their shape and how flat it lays. I think it is largely because of the above.
I get flyers made out of thicker paper in the mail daily advertising sales, politics, etc., (e.g., Joanna fabrics/Michaels crafts) that I use for my hexi paper. They work great and are free!