There’s no real risk from granting Safari access to any file. Apple generally tries to restrict what isn’t necessary, and that can sweep in cases like this.

If you keep Chrome up-to-date without changing any settings, any PDF you download may open within the web browser by default.

Creating a keyboard shortcut that opens your browser to the Google Docs upload option won't save you a lot of time, but you'll more easily transmit files as e-mail attachments.