Most shotgun firing pins aren't too complicated to make on a lathe, especially if you have the pieces of the broken original for correct dimensions. Depending upon the make, original replacements may be found from Numrich or other parts dealers for less than the cost of a machinist to make one.
I've made a couple using common O-1 tool steel, and then hardened and tempered them. Some say the hardening and drawing is not really necessary. But I've seen a number of pins that mushroomed on the rear end due to being too soft.
Others say they have successfully had broken firing pins repaired by welding. However, welding tool steel has the risk of soon cracking again due to the high carbon content. It's also likely the weld repair will need to be cleaned up on a lathe anyway. For that reason, I'd go with making a new pin if replacements aren't readily available.
