The fastest way to do this is to just delete the files that supply the spatial information related to the raster. If the image is stored as a tiff or you can just open up the folder it's stored in and delete all the files except the actual image. Then give that file to the students.
Looking at the image below, you would delete everything except the highlighted file, then distribute that.
I'm not certain how this would work with other raster formats that encapsulate the spatial information but you could always just export them to a tiff and then use this technique.