Hi Deanna,
I just leave them in my mailbox, and haven't bothered to delete them.
Is your inbox running out of space?
My PayPal emails go to different email from shop email, so I just keep them there too. I don't create shipping label.
I think you can delete the emails because you can still retrieve the records from PayPal website and the sale records are on Etsy orders page anyway!
I've never had a need to refer to the emails so far. I just keep them cos I haven't bothered to delete them, hehe.
Hope that helps!
- Khin