Hi-HooYah!
You're gonna think I am nuts! How thick are we talking? The reason I ask about the thickness, I have found a tool that works for me. It is no bigger than a "chopper" tool from Short Line. It is a small little cutter. Now this is where it gets weird. You remember the big Guillotine blade, paper cutters from businesses and schools?
Well this is a junior version. It even has a little drawer underneath for replicated parts. It will cut up to .030 thickness. Any thicker and it starts to wander. Remember this is for the home crafter though. You know, like paper flowers and stuff like that.
It works incredibly well for any small cuts below 4"x6". I have been using mine to cut the small constructs out on the paper models so the lines are straight! It does work well for thinner plastic for maritime scratchbuilding too.
Be warned though. I use edged triangles and clamps for thicker stuff. I have what I call a " Hook" I made from a carpet knife for thicker stuff. The old hook is getting up in years though. I bought a new one and am just now getting the blade shaped where I need it to be. Then Grinding, shaping and stropping with a lot of " Jewelers Rouge" On leather!
I find most of the commercially made products a little bit less than what I need. Last thing you want when making showcases, even out of styrene as thin and brittle as C.D. cases is a weak blade that twists and wanders. So, go for the original suggestion. and I think you will be glad. I got mine at Micheal's. I think H.L. and Joann's carries them too.