the first 2 links are fine, best to replace IDC's with crimp type (as suggested above).
the 3rd link isn't the right pin, I suggest (as suggested above) https://www.marcospecialties.com/pinball-parts/CT156T
and the keying plug https://www.marcospecialties.com/pinball-parts/CF156K
the desoldering I imagine to be the hardest for you if you haven't done any soldering/desoldering.
cutting the old header pins off might help as there will be less heat dissipation.
you'll be heating the solder up so as to suck it out with either an manual or electromechanical/electric desolderer, and some solder suck wire with flux will help.
try not concentrate the tip of soldering iron directly on the solder pad, but rest/put it against both the end of the pin and the solder pad, ideally you will see the solder change colour and melt sand it's at this point you want to put your solder sucker over this area and release the solder sucker to hopefullypull all the solder out leaving it clean of solder, but should some remain is where solder suck wire comes in handy as you place it over the same area, against the pin and the solder pad then rest the soldering iron tip on the copper wire and as it heats up and with it being flux infused it will/should draw out any excess solder.
you don't want to remove the solder pad from the board, nor pull out the through hole trace.
good luck!