The Pitmen enjoyed a famous run to the fourth round as a fifth-tier side in 1996-97, defeating Blackpool and York City before losing 3-2 to Premier League Middlesbrough at the Riverside Stadium.
Almost 27 years on from that feat and Hednesford are now competing in the Northern Premier League West Division, the eighth tier of English football.
King's team have come through five rounds to reach this stage of the competition, where they will now face National League outfit Gateshead in front of the television cameras.
Injuries and suspensions hit Hednesford
Heavily financed by new owners who took over the club earlier this year, Hednesford are gaining widespread attention in non-league, but King will likely be missing five key players on Saturday.
Blaine Rowe, Joel Taylor and Korey Roberts - three of his first-choice back four - as well as midfielder Sion Spence are injured, while the well-travelled Jake Jervis is suspended.
Speaking to the Express & Star, King said: "We've got a number of injuries and I just hope we can get a side out.
"We will give it our best shot. The FA Cup that's what it's made of, to bring out the best."
On Gateshead, he added: "Gateshead is a proper challenge. The achievement is doing what we have so far and if we can get to the first round then we've done amazingly.
"We couldn't have got a worse draw, they're the best side in my opinion."
"We can't take our foot off the gas'
As far as Gateshead are concerned, they are still adapting to head coach Rob Elliot leaving for League One side Crawley Town, with Ben Clark being put in interim charge.
Greg Olley, the club captain who is sidelined with a broken leg, is also part of the management team that have overseen a 1-0 win over Wealdstone and 2-1 defeat at Tamworth since their promotion in the dugout.
With Gateshead sitting fourth in the National League standings and Hednesford down in 15th in their division, there are 81 places separating the two teams in the English football pyramid.
Nevertheless, Olley is sensing an opportunity for the Heed to shake off their recent below-par performances on their second trip to Staffordshire in the space of four days.
Commenting on Gateshead's official website, Olley said: "We know they're a good team, they've got a good backing behind them so we can't take our foot off the gas.
"We need to go there and put the last couple of games, where we haven't been quite at it, to bed and move on from that. We are looking to go down there, win, progress and go into the hat."
These two teams have not squared off since the 2012-13 campaign when Gateshead prevailed 4-1 in the FA Trophy.