Safely Offering Downloadble Files

I would like to pick your brains, if I may, knowing how many people here do this sort of thing, so surely someone will be able to help solve my dilemma.

I sell digital images via a marketplace type site. At the moment I am emailing the files to my customers. I don't like to have more than 10mb attached to an email, because I believe some people's email clients dislike that.

So at the moment a single set of textures can require between 1 and 6 emails/attachments to send.

Many customers buy more than one pack at once (I have bundle offers for 4 or 5 packs). And I get multiple orders in a day. Most of my orders occur during the night (as from American market, I am in the UK) so I wake up to them. And want to get them to the customers as fast as possible, of course.

I have an idea of how to improve this, but I am not sure if is a good one, or even safe to do.

I could upload all my graphics files to my webhost, and give them random, non-sequential names. I keep a master list of which name is which.

When a customer orders, I send them a single email with hyperlinks to the relevant files.

Every so often I change the names of big selling files, just in case.

I obviously don't want a customer to be able to access all the graphics, but also don't want to make them have to work hard to get the ones they have legitimately bought from me.

I would appreciate your thoughts on this, and if you have other, better solutions, I would be very interested to hear them. Thank you.