Do you know how to launch an application from Hypercard? I've never used Hypercard, but it seems that if you could launch an application, you could just have it launch an AppleScript in the same way, then have the AppleScript take care of all the file moving.

I am still not sure what will happen when you move the file into the printer. Normally when you drag a file onto a printer, it creates a print job without literally moving the file into the printer. Whereas if you specifically move the file into the printer, something might happen similar to when you attempt the drag and drop with extensions off. (File physically moves into the printer and doesn't print.)

I'd check and see if there's an AppleScript Dictionary in the Print Monitor or Desktop Print Monitor extensions. Maybe there's a command that will do just what you want! It seems like a thing people would often want to do.