Forgotten firmware password

I have a 2011 MacBook Air 13 inch on which I set a firmware password many years ago. All went until an OS update failed and my MacBook could not be restarted. I then found that, although I had made a note of my firmware password, it had got lost over the years. I now have a replacement machine, but there are photos on my old machine that I would like to be able to recover. I am aware that I may be able to get this fixed at a Genius Bar, but the only proof I have now of my purchase ( which was in the USA) is a copy of my application for Apple Care Protection. Will this suffice, and will I have to leave my machine at the Apple Store for removal of the password?