The visitors picked up a victory in their opening game of the season on Saturday, while Stockport have won one and lost one of their first two games.
Stockport suffered playoff semi-final heartbreak at the end of last season and started the new campaign with a disappointing 3-1 loss at home to Dagenham & Redbridge.
However, the Hatters hit back on Saturday with a 1-0 win at Southend United through John Rooney's first-half strike at Roots Hall.
Simon Rusk's side now head back to Edgeley Park, though they do not exactly have the best of records there, failing to win any of their last five league matches on home soil.
Grimsby will be looking to prolong Stockport's winless home run when they make the two-hour journey west on Tuesday.
The Mariners dropped back into non-league in April after a five-year stay in the English Football League, and the aim will be to make an immediate return to the fourth tier.
Town are already playing catch up after their opening game of the season against Bromley was postponed due to some confirmed coronavirus cases in their camp.
The delayed start to Grimsby's campaign was good news for striker Ryan Taylor, who won his race to be fit for the win over Weymouth.
Hurst is unlikely to tinker with his starting lineup too much in midweek, though Lenell John-Lewis could come into the side in place of Taylor, who is not yet fully fit.
As for Stockport, Scott Quigley and Raikhy will be confident of retaining their places in the side after earning their first-team debuts in the rare away win at Southend.
Stockport County possible starting lineup:
Hinchcliffe; Rydel, Keane, Rooney, Barclay; Palmer, Southam-Hales, Raikhy, Croasdale; Quigley, Madden
Grimsby Town possible starting lineup:
McKeown; Efete, Crookes, Fox, Longe-King; Hunt, Pearson, Esteves Sousa, Clifton; John-Lewis, McAtee
We say: Stockport County 2-2 Grimsby Town
New-look Grimsby made a belated start to their campaign with all three points against Weymouth and were good value for that victory.
It may take time for Town to fully click, however, and we can see last season's beaten playoff semi-finalists Stockport taking a point from this game.