Just discovered broken wires coming out of my distributor. Can I replace them?

No not a problem RRR; that is why I said earlier to solder the wires. The p/up wires can be very long. They are on BB cars with the ECU often mounted on the inner guard; p/up wires have to go from there to the dist, at the front of the engine. The induced current in the p/up wires is very small, such that the resistance would need to be very high before it caused a problem. Another example is the MSD 'box' igns; you can buy an 'extension' harness for the p/up wires if the box is mounted a long way from the dist.