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It depends on the type of show you are attending. If it is a "show and shine" type event than anything goes; just bring what you have. If it's an NCRS type event, then your corvette will have to be configured the way it came off the assembly line to compete.
Replacing a battery on a 1963 Corvette is very easy to do. There are two clamps that need to be taken off that are holding the battery in place. After the clamps are removed, take the battery cables off and lift the old battery up and replace it with a new one.