Is there a way to have a Send Email button on an Activity?
It's likely that someone has written an extension to do this but if there isn't one in the extension directory (I presume that you've looked) then you have to assume that no-one has taken the time to publish it.

I suppose I could end the answer there, but here's a bit more thought on how you would develop it...

Since this is a fairly reasonable thing to expect to do, would be fairly easy to implement just adding a link to a URL of the format civicrm/activity/email/add?action=add&amp;reset=1&amp;cid=[CID]&amp;selectedChild=activity&amp;atype=[ATYPEID] and an addition that is unlikely to break anything, then it might make sense as an addition to core. (I'm not sure we've worked out exactly how to draw the line on how to add it / this one seems borderline).

Implementing as an extension would be a good first step.

Note: adding the text of the incoming email would be a little harder, and need a bit more thought, though there would be a fairly straight forward way to do that - it's not rocket science.