Do you have the Fiskars rotary or wire? I have the rotary and it is awesome! I love mine so much I bought a second one for my crop wagon that is always ready to run out the door with me.
I haven't tried the wire but the rotary works so well for me I stick with it. I do have to hold my paper in place but it is no big deal. I think all of them are going to require you to hold the paper in place but mine has more than just a little bump. The bump on mine is substantial enough that I don't have any problems and there are bumps or ridges on both sides.