I can confirm that the cal key is the same for all the multimeters and the 4700 calibrator.
I actually had a key that was close, it went into the lock OK so I pulled the switch apart to figure out where to file the key to get it to work, from that I had a few more cut for my devices, I covered it in a video of mine on a 1062 if I remember rightly.
attached is a photo of the key I found on the forum some time ago, it is almost the same.
My key is an CH751, and the ones I had cut are a ilco N54G type.
Here is the video where I pull the lock apart: