A file cannot delete itself.
But FileMaker can delete other files--such as other FileMaker files--provided the following requirements can be met:
The file must be in a location where the user's permissions allow them to delete the file
The file must be closed.
The filepath to that file must be known.
If all of that is met, you can use Export Field Contents, with the path, but no field specified, to delete the file.
But your design seems very cumbersome. Instead of having multiple files, I suggest having multiple record sets in the same file, in the same tables. Then deleting unwanted copies of this data becomes the simple process of deleting records instead of files.
I agree it is cumbersome but it is how the boss wants the system set up, the original database contains sensitive information while the exports all contain only a snapshot of the data allowing the forecasts to be used in public meetings and sent to particular members of staff without having to worry about permissions for particular sets of data.
Did as you suggested and it works a treat, script holds a variable of the filename, opens the main database and from there it deletes the file at the variable path.