Hi ggsalas,
I took a look at your question. I don't think you need to worry about that, because potential attackers/breachers would have to know the attachment number (1268743374-wv5r7484), and if the parent folder is protected, it would be extremely difficult for them to retrieve it. For instance, when I view the source code of the parent page, the number is not appearing and there are no signs that the page even has attachments.
I hope this helps. If it doesn't, and you still want extra protection, I suggest you look into online security software (there are a lot of options out there for what you're trying to accomplish). Since I don't use one myself, I wouldn't know which one to recommend you.
Cheers!