That seems like a better approach to me. With email, you're at best exposing a disk-filling service to the internet and most likely looking at exploits running on servers with a fair amount of interesting data. There's also a fun race condition between the time a file is scanned and when someone opens it, which isn't as solved a problem as it should be.

With requesting that people send you a URL, you're in control of when and where it's accessed and things like Safe Browsing are visible to the recipient.