Two options come to mind:
Option 1, There's a little check box down at the bottom of your script editor labeled "run script with full access priviledges". If you click that, your script will run and delete files for all uses just as though they had opened the database with a full access password. I believe filemaker added this feature specifically to resolve issues like you describe.
Option 2, This is "Ye olde fashioned way" but it still has uses in some areas. Define global fields for each field for your users to fill in their criteria. To "commit" the data, use a series of set field steps to update the fields in the current record (and yes, you can create new related records this way as well.) If the user chooses to cancel, you don't do anything expect possibly clear the global fields since you haven't yet modified anything but global fields.
Duh! I've seen that box a million times. Should have tried that before posting .... I'll go try it now.