Replating probably isn't necessary if you just want to shave with it. If you want to get it replated, the old finish that's got the pits in it would have to be stripped first.
Pitting of metal is common, particular in areas of extreme moisture. My understanding is moisture intrusion leads to rust and corrosion, and the pitting results from flaking off of corroded/rust bits. Depending on how deep the scarring, sanding is required to reduce or minimize the pitting.
I tend to believe a 50+ year old razor with a bit of pitting is a good thing. After all, I'm 50+ years old and I have a lot of pitting.