Removing WP install subdirectory from media file URLs

I’ve installed WP into a sub-directory for a basic level of “Security through Obscurity” that has been recommended to me many times. Everything works, I’ve done this for several sites, and I understand this isn’t a fool-proof method of security by any means.

However, the sub-directory does bring up a problem. For instance, a client of mine will be sending out press releases with links to download PDFs and such. These URLs end up looking weird and unprofessional:

www.mydomain.com/somerandomstuff/wp-content/uploads/…

The sub-dir helps a bit with security but it leads to some messiness with URLs so I’m wondering if there’s a way to remove the sub-directory from media file URLs. Can these be re-written using htaccess? Will I need to resort to a plug-in? Any solutions?

Thanks in advance.