Robert, I tried that and it did not work
Here is how my navigation widget is defined in my main app:
 <navigation:NavigationWidget  left="12" top="20"  id="navigationwidget"   /> 
So everytime I activate the drawtool I had
navigationwidget.map = "";
and when I deactivated the drawtool I had
navigationwidget.map = myMap;
But I got this run-time error:
TypeError: Error #1009: Cannot access a property or method of a null object reference.
 at com.esri.Navigation::Navigation/changeNavigation()
 at com.esri.Navigation::Navigation/doNavAction()
 at com.esri.Navigation::Navigation/buttonbar1_valueCommitHandler()
 at com.esri.Navigation::Navigation/__btnBar_valueCommit()
 at flash.events::EventDispatcher/dispatchEventFunction()
 at flash.events::EventDispatcher/dispatchEvent()
 at mx.core::UIComponent/dispatchEvent()
 at spark.components.supportClasses::ListBase/commitSelection()
 at spark.components.supportClasses::ListBase/commitProperties()
 at spark.components.supportClasses::ButtonBarBase/commitProperties()
 at mx.core::UIComponent/validateProperties()
 at mx.managers::LayoutManager/validateProperties()
 at mx.managers::LayoutManager/doPhasedInstantiation()
 at mx.managers::LayoutManager/doPhasedInstantiationCallback()
Thanks for any help you can provide!