If you do decide to use the mouse I think the best way to do it would be to make the helicopter move simply camera-relative.. (where pressing up/down/left/right will always move the helicopter in that direction relative to the screen, regardless of the helicopters angle)
Also, you can smooth out and limit the rotational speed in a similar way you smooth out directions and limit their move speed.
Instead of setting the heli's angle to the mouse, set a variable 'targetangle' to the mouse... and have the heli.angle move towards that gradually using one of ..many.. methods..