All disk brake Corvettes ('63 and '64 too) were equipped with tapered roller bearings at all four corners. If the front bearings are in good condition upon inspection after cleaning, I would suggest properly packing them with a high drop point grease designed for disk brakes and reusing them. If you take apart the rear spindle pack is is probably a good idea to replace the bearings as the cost of the bearing is small compared to the labor, however, a technician with experience and/or close adherance to shop manual procedures is required as a shim must be select fitted, the the pack torqued to the proper value, and final end play checked to be within spec.
Duke
Duke