I shop for the stuff at Asian markets and I can buy the papaya already shredded. It's really more a fine julienne, than what I would typically call shredded.
In Thailand, they will whack it a million times with a cleaver or knife and then peel it with a peeler. you can probably find videos of that on YouTube. You can also use a mandolin with an attachment for creating julienne strips. Watch this:
https://m.youtube.com/watch?v=7Wz4HVCNKr4