Micrometer, vernier calliper, screw guage, or fabric thickness meter can also be used take multiple readings and average out for calculation of mechanical properties.
Contactless laser measurement would be ideal because of the compression and cutting problems but if it's not available. I would say you can get close results by using a simple microscope and use 5 to 7 crossectional samples from different parts of the web. Don't forget to use some very good cutting method.