How old? There's no such thing as a Handi Shotgun, Handi-rifles are .... rifles.
It makes a difference if it has a transfer bar, vintage single shots prior to 1978 had rebounding hammers and are simple to replace the firing pin just by removing the top pin or in the case of even older models like the 19XX models just a screw, later with transfer bars require the trigger group be removed to allow the transfer bar to drop out of the way...unless it's broken and needs to be replaced anyway. Pins are splined on the left side, so they need to be removed right to left. Use the trigger information in the FAQs for later transfer bar model R&R, although they don't cover the firing pin, the trigger group info is covered.
Tim