One way to dispose of a file in a 100% reliable manner is to keep it on a separate HDD partition you can purge, or, better yet, on a separate medium you can afford to destroy.
If that's not practical, a good compromise is to make sure the file is only stored encrypted. When you need to "destroy" it, all you have to do is to forget the key. You don't have to care about edge cases leading to the file not being fully overwritten.
The next less secure alternative is to use a file shredder that you trust. If it's implemented correctly, it will track every sector on the disk associated with the file and overwrite it. Of course, it will not be able to destroy any copies of data that you, your OS, or your storage controller have made that it doesn't know about (think temporary files, swap, disk defragmentation, etc.). In general, it only makes sense to pay for a tool that was subject to a security audit.
Then comes your idea of simply overwriting the file. It's not 100% secure, but it will for sure make the data unrecoverable using off-the-shelf undelete tools. That's actually sufficient in many practical situations.