Then you could add
Koreader to your device, its OPDS lets you access the calibre server, from your device. Since you can tell it where to put the file, there is nothing stopping you from putting the file where the stock readers can see it. No browser needed.
With Koreader you can also connect to calibre as a device, wirelessly, and send selected books from calibre's library to your device. With this approach calibre will create its file structure on your device (again where you tell it).
You can wirelessly "pull" ebooks from calibre on your PC, to your device, from your device or wirelessly "push" ebooks to your wirelessly attached device, from within calibre. (I think just turning the calibre server on and then using the OPDS feature of Koreader on my device, is the easiest. I usually have calibre open, from processing a new book, anyway. )
As for "The Cloud"
this is one way, just don't use a "Public" folder.
Luck;
Ken