The Pitmen will make the trip to Stamford in Lincolnshire from the Northern Premier League.
Stamford sit 21st in the league and made it through to the next round with a 4-2 win over fellow Northern Premier League side Ashton United on Saturday.
Scott Smith, joint chairman of the Hednesford Supporters Association, believes the club will be happy with the draw.
He said: “If we get through on Tuesday then it has to be one we are happy with.
“It is a good chance of getting into the first round proper.
“But away games are hard. We have nothing to win, we go there and we are there to be beaten because we have a bigger league status.”
The Pitmen’s replay away at West Auckland takes place tomorrow night (October 15).
The two sides drew 2-2 at Keys Park on Saturday with goals from Nathan Woofle and Neil Harvey.
An injury time equaliser from Lewis Galphin sent the Pitmen into a replay.
“The lads will be fired up for it,” added Smith.
“Don’t get me wrong, it is a good result for them getting a draw. But they did celebrate as though they had won the game.
“It’s not ideal. It is a long trip and an early start but we have to do it.”
The Pitmen are just two wins away from a potential FA Cup 1st round proper tie against the like of Wolverhampton Wanderers, Sheffield United and Preston North End.
Smith added: “Wolves are my other team so why not?
“They are the biggest team you could draw. I would love it if we played them either at Keys Park or at Molinuex, it would be superb and we would get loads of media coverage.
“My friends would say who I would support and I would support Hednesford.”
Staffordshire’s other side in the FA Cup 4th qualifying round Tamworth will welcome local rivals Soilhull Moors to the Lamb.
Games to be played on Saturday October 26.