A more stretchy printable paper alternative?
How about tricot? That should be stretchy enough.
You could, for instance, print on a T-shirt, if you're fortunate enough to have a printer that can do the job. Or else there are companies offering to print a given image on a T-shirt.Be aware that edges may fray and/or curl, but good glue should prevent/solve that issue. 
Make sure the size of the print is not that much different for the size of the globe. The less you have to stretch the tricot, the less you will look through the holes in the fabric, and the less stretched out the details are.I hope this gives you some inspiration.