I have heard from some users that Neo's SafeKeys cannot drag and drop to the Opera web browser.
I have done some investigation into Opera; both testing and extensive online research.
In short, the Windows version of Opera does not allow dragging and dropping between itself, and any other application. Opera will only allow dragging and dropping within itself.
This is not a Neo's SafeKeys problem, as any application would have a issue with this.
Probably the only hope would be to lobby Opera itself, to get them to allow dragging and dropping from other applications to Opera.
Here are two postings on the forums that explain the dragging and dropping limitations (in various ways):
http://my.opera.com/community/forums/topic.dml?id=253332
http://my.opera.com/community/forums/topic.dml?id=249292
(I'm sure there are more).
Hope this helps explain things.
Neo.