ArcToolbox > Conversion Tools > To Shapefile > Feature Class To Shapefile (multiple)
Click on the ' Environments...' button at the bottom of the dialog box. To the right of the 'OK' button.
Click on the 'General Settings' text.
You should see two fields marked 'Output has Z Values' and 'Output has M Values'.
Set both fields to 'Disabled'.
You should now have copies of your original shapefiles, without Z & M values in your new folder.