Attachments should work, with a few caveats. Due to some annoying quirks of the HTML5 FileSystem API, there's a whitelist of supported file extensions. This includes everything useful we could think of, but it's not exhaustive.
The specific requirement for being whitelisted is that it shouldn't have a MIME type that Chrome wants to open inline. Give me a list of extensions that you'd like to see supported and I'll see what I can do.
Screensavers are just special exes on Windows and are commonly used as viruses. Might be better not to whitelist that one and instead convince people to zip them up if they really want to send them.
I think that there are a fair number of mail filters that block .scr entirely, anyhow. In that respect, they're similar to .bat, .vbs, .wsh and the like.
Alternatively, you can just offer to automatically zip those for the user. Actually, that might be a good idea for all unrecognized files because it avoids a lot of weird problems with funny extensions that are automatically blocked.
As a developer who sometimes have to send a zipped project with a compiled build inside, I find this "feature" extremely annoying. I usually end up renaming the file from .zip to .lol or similar.
Attachments should work, with a few caveats. Due to some annoying quirks of the HTML5 FileSystem API, there's a whitelist of supported file extensions. This includes everything useful we could think of, but it's not exhaustive.