Apparently one way Tearaway Unfolded will bridge the gap is with an app. It’ll handle the actual papercraft you do in-game if you have an appropriate device. Otherwise I imagine you’ll have to struggle with the weird PS4 touch pad.
According to the European PlayStation Blog, “Using the app, you can access the cutting mat to cut out new creations, customise your characters, re-texture the world with photos and collaborate on creative challenges! Everything you create using the app is sent directly into the game, instantly appearing in whatever scene you’re currently playing.”