Is the schema always the same? If so, you could probably make an empty shapefile in arcgis or qgis and the use a filecopy writer to rename it.

If your schema's aren't identical, you can write the shapefiles you are currently creating to a temporary location then copy them and delete the features using arcpy to your final location

Thanks for answers !

I didn't know the filecopy writer. I'm looking on it and I guess that will be my solution. I'll try it this monday.