There isn't a way to turn them all off. You can show the active path (for the current tween), or for all tweens by choosing Always Show Motion Paths. So I'd make sure that Always Show Motion Paths is off (select a tween, access this in the Motion Property Inspector panel menu). So it is possible to just show one at a time.
The only way to work around not showing the single motion path is to make the layer outline color the same as your stage. You can also lock the layer to get rid of the dots.
Do you have a use case when seeing one motion path gets in the way of your work? (Just so I can bring it up with the team - they'll ask for the reported use case).