1968 was when grounded 3 prong outlets became required by electrical code. I also see "made in west germany" on that spool. That would date it from 1955+. I'd say sometime in the mid 1970's though because my basement was renovated in September 1978, and the bathroom fixture has a glass shade with that exact same pattern on it.
The wires look in very very good shape, they actually might be a retardant cotton or rayon braid and not asbestos, but lop that nasty splice off the end of the hot wire before connecting new wires in, and be very careful with that cracked glass shade.
You might not have to rewire. I'd say give it a trial run with the original wires for a few months of use and check it again for any wear spots. For me I would replace the wiring just because I'm paranoid over electricity, but then again all the wiring in my house is from the 1950's so go figure. Wiring does accumulate more heat though when coiled up, and the old cotton sheathing didn't do much at alleviating that problem.
Good luck!