Thanks for the suggestions.
I'm surprised that there doesn't seem to be an obvious solution since this is something that will affect a lot of websites that sell digital products. It may seem odd to us webmasters that some people don't own a computer, but the request from customers to download directly to their phone will only increase.
Yes, Apple are very restrictive with their iPhone. I think it's also the case that you need a computer for the iPad. I don't own an iPad so I'm unsure. I don't know about other smartphones or tablets.
Of course we could develop an app and sell it via their store. But then they'd be taking a hefty commission. It's one thing to pay commission when you're getting new customers that might not have heard of our website, but that's not the case here.
I don't know if there's a workaround by having an app that's free, which acts as an audio player but will only play if the user has entered a serial number - which of course they'd purchase from us. Although I'm sure that'd be against the TOS of most app stores.