Don't dry fire the Mark III or later Colt's, the firing pin can break.
Replacement requires a special press device and support dies to press the old pin out, and to press the new pin in.
Also the job needs a special staking punch that works down the barrel to re-stake the thin "skirt" of metal around the recoil plate.
Attempting a change with a punch and hammer can ruin the frame.
Since Colt no longer services any of the older models, you have to send it to Frank Glenn or Len Specklin at Spartan Firearms.