Well, in the movie we're doing, the first thing we have to do is actually hide the current, old-fashioned mouse cursor.
With the Actions panel open, select the Add Action menu (a "+" symbol on the top left corner of the window), then select Objects, then Mouse, and then Hide (see image).
Since you were editing the actions of a frame, and now this frame contains a "Mouse.hide()" action (no parameters are necessary), every time your movie starts, it will automatically hide the mouse cursor.