Agree it is best done off the engine to keep the chips out of the coolant. Since the threads are tapered you should be able to run the tap a little deeper than original and restore adequate threads. It will take some care to get the tap started right.

A good hardware store will have individual PT taps. Or get a complete set at HF for reasonable cost. I have found the HF taps to be fine for clean up and touch up work.

If you decide to tackle the other nipple while it is out heat helps... heat the nipple cherry red and touch a candle to it while hot. Let cool and it should come right out.