https://graph.facebook.com/*Facebook id*/picture
will translate to an Akamai link which still contains the Facebook id. You can try saving all the photos... but that's not really worth it and you will have to re-save to keep up with the latest version of https://graph.facebook.com/*Facebook id*/picture
Even then, since a user's main profile picture is publicly available, it will likely be cached by Google so one can do a Google Image search against the picture you tried to obfuscate.
So no, there is no way to hide this information