How to point a static url to a file
You could setup a template at /menu that grabs the PDF you want and redirects with a 302 (not a 301 since it isn't permanent).

The URL would change, but that might be ok if you only care about having an easy link to share.

If redirecting is a deal breaker, you could make a small plugin that returns the file with proper headings, then call that from the /menu template.