Estel, the cheap vacuum form plastic would turn soft with a hair dryer and not endanger the cover when stretched over. I remember seeing a vacuum forming machine at a model airplane shop when I was a kid not sure how common the real deal is though vs the plastic sheet and a hair dryer.
I got a nice enough aesthetic effect on my wife's phone using vinyl electrical tape stretched to under the cover and then extra secured by first cleaning and then laying doen some Scotch brand double side sticky tape.