Here is a parts list showing the two piece pin, part numbers 4 (front) and 4A (back). The picture seems to show the front part as having a flat, but it is just a round pin with a head to compress the spring.
I tried a Colt firing pin but it is too small and retaining it would be "iffy". I still think, though, that a two piece pin is the way to go in that confined slide.
It is odd, but yours is different from mine, and both are different from that shown in the "vestpockets" web site. The latter has an enlarged head, which mine does not. Mine has three diameters, the full size at the rear, a short reduced section, then a fairly long small section at the front, where yours has only two diameters. I have no idea if mine or yours is a replacement, or if there were different types.
With yours broken, you might have had no trouble removing it. I really can't believe they intended that the back plug be removed to get out the firing pin. Those manufacturing holes (it was needed for drilling the firing pin hole) are usually plugged up solidly and intended to be a permanent assembly.
You might talk to your gunsmith about just making a pin. Another possibility is to see if there is a small machineshop in your area that might make it.
You could make it out of soft metal, like out of a nail, if you don't plan to fire the gun more than a few shots. A drill or drill press and a file can be used to turn it down where it has to be smaller. Yours looks like there is no provision for a spring, but there should be and if you make one or have one made, you should have a smaller front section to allow for a spring. A spring can be bought at most hardware or big box stores and cut as needed.
Normally, firing pins are made out of tool steel (drill rod) and then heat treated for hardness, but for a non-using gun, soft metal will work OK.