BB FlashBack can hide the mouse cursor during playback. You can select a series of frames and choose to hide the cursor in those frames when the movie is played back.
How to hide the mouse cursor:
Select the frames in which you want to hide the mouse.
In the Actions menu, select Cursor -> Hide the mouse cursor
The selected frames will be drawn in blue in the mouse bar, indicating that the mouse is hidden in those frames.
To un-hide the cursor in those frames just select the frame and select Actions -> Cursor -> Show the mouse cursor.