When you click Email to send the activity via email, I don't actually open the email app. I just go and tell Android that I want to send a file. Android will ask you to choose the app you want to use, and I would normally use Gmail.
However, there are other apps which can accept files. Dropbox is one of those, if you have the app installed. So if you want to share on Dropbox, just click email and then choose "Add to Dropbox".
This trick will probably work for many other apps which can accept a file in input. I will update the wording in one of the next releases to reflect the fact that "email" isn't actually limited to send an email :-).