You don't need a special socket just whatever you already have that fits, or off the shelf that fits.
Judging by what I can see on the front axle/wheels you have 10 lug on 7.25" bolt circle hub centered wheels, not stud centered Budd wheels. I don't expect you have any left hand threads either. If I'm wrong or confused please share more detailed pictures.
Socket might be anything between 15/16 and 1-1/8" depending on what nuts were used, I don't recall off hand the factory hex size on the standard 5/8" fine thread lug nuts.
Grigg
