This will remove the basemaps, but will leave the widgets in place.
In Config.xml, comment out the menuMap statement by replacing it with this line:
<!--menu id="menuMap" visible="true" icon="com/esri/solutions/flexviewer/assets/images/icons/i_globe.png">Map</menu-->
...then add this line below it.
<menu id="menuLayers" visible="true" icon="com/esri/solutions/flexviewer/assets/images/icons/i_globe.png">Map</menu>
Now, search for the widgets that have the statement menu="menuMap", and change it to menu="menuLayers"
Rick